From a purely academic perspective, I agree with @aquapt – Centre stands out as the best option on your list. It’s a very solid school that gets less attention than it deserves due to its Kentucky location.
Centre is the strongest school on the list, academically, but it has neither business nor engineering programs, so if you’re specifically planning to focus on business it might not satisfy your goals for a business-oriented year abroad. But if their economics and finance program would meet your needs https://www.centre.edu/majors-minors/economics-finance/ , then definitely consider Centre; it’s a standout on this list and an excellent school. The US News analysis of undergraduate teaching at liberal arts colleges has Centre ranked 9th in the nation, tied with Williams, the LAC ranked #1 overall in the country. About 40% participate in Greek life so that’s a major aspect of the social and party scene, since the town is quite small and Lexington, the nearest city, is 30 miles away. There’s both D3 and intramural football.
Coe is also a standout; it’s a bit less competitive than Centre but it does have majors in business, international business, and accounting. It’s a very solid choice academically, and Cedar Rapids has a lot to offer as a college town. Publisher’s point that Coe is not on as solid financial footing as some others is well taken, but that wouldn’t worry me too much for a one-year commitment. 86% of Coe’s students live on campus, so you would definitely get the residential campus experience. Greek life is a little less prominent at Coe than at Centre but still present, with about 25% participating. Downtown Cedar Rapids is very close by and a great town. Also, if you’re interested in the upcoming US presidential election process, being in Iowa next year could be very interesting as the Iowa Caucuses kick off the primary elections for each party - they attract all of the candidates and a great deal of attention.
The two urban schools that I would consider are Catholic U in DC, and U of St. Thomas in Houston. Both are in very nice sections of major US cities, with great night life and lots of students from other nearby colleges in addition to their own campus life. Houston and DC are very different in both weather and character. A lot of students in DC are there specifically because they’re interested in government/politics and want to be in the nation’s capital. Houston is the 5th largest city in the US - an extremely diverse, liberal-leaning city despite the overall conservatism of Texas - and is relatively affordable compared to the east coast cities. Both of these colleges have business schools (although neither business school is prestigious enough to have a ranked MBA program). Would you be guaranteed on-campus housing at both? (You do not want to have to find your own housing in DC, and even in Houston, living in the trendy Montrose neighborhood around UST is pricey compared to living on campus.) UST is considerably more diverse than Catholic U. (27% white, vs. almost 70% at Catholic U.) and has more international students as well. Entering student stats aren’t much different between the two, and the stated philosophies of the business schools are nearly identical (business with a Catholic moral/ethical focus). Both cities are major airline hubs and easy to travel to. If you want a big city college experience, I would weigh those two options. Catholic is better-known and a shorter trip for you, with potential to explore the whole eastern seaboard, so it’s probably the default winner… but UST and Houston have their own strengths that could potentially sway you the other way. (Other cities in easy travel range of Houston include San Antonio, Austin, Dallas, and New Orleans… plus the gulf coast beaches are close by.)
Nothing else on your list jumps out at me as offering more than those four do, unless there’s a specific location you’re more interested in, or if you felt you would enjoy the unique college experience of Warren Wilson, with its focus on campus work assignments and community service. The Asheville area is lovely and the educational model of Warren Wilson is innovative, but you sound as if you may be looking for a more traditional/mainstream US college experience.
Can you get your hands on the Fiske Guide? That usually does a good job summarizing the feel of many campuses.
I’m familiar with a couple of these that are in the midwest US. I know kids and family who have attended some of these colleges, and are doing well in life; so i’m not as concerned about the education you’d receive; rather than the experiences. The Midwest is HUGE, can be sparsely populated and often very remote - small towns in the middle of prairies and hours away from big towns with very few transportation options. (eg: Hastings & Dakota Wesleyan)
Many of these colleges in small towns might offer some parties, but to go out to bars you need to be 21. . . . If you’re not 21 i’d stay away from the super small schools.
some of these colleges are also christian colleges, and you won’t find many parties on campus or around campus. Like Whitworth in Spokane. Pretty Pretty location, but not a party school. Nebraska Wesleyan is in Lincoln, NE which is a pretty fun college town as UNL is there.
I like living in the midwest. But if it were me looking to attend these schools from the UK, I’d focus the location on the east coast, where there’s good transportation, lots of history to see and lots of people and action.
Another vote for Catholic. Being in Washington DC would be a great location for study abroad, easy to get to, and easy to travel from to see other parts of the US.
The US is huge and it has more than 2,000 colleges and universities, many of them located in the middle of nowhere. They’re not schools our kids would consider, and I certainly wouldn’t recommend many of them. Pick an exciting location and a school big enough to attract many different kinds of kids. Personally, I think this is a no-brainer: Catholic University will offer you the most interesting experience. Plus, it’s located in a part of the country that has public transportation, so you can travel & explore a vaibrant part of the US. That can’t be said about many of the schools on your list.
Clarke University is not Clark University. It sounds like “privatebanker” may have mixed the two by his “near Boston” description.
Catholic University sounds like a great idea for reasons “privatbanker” has listed.
Another vote for Catholic U. That was actually my first choice school, but the financial aid was terrible.
Are you Catholic? Are you okay going to an officially Vatican endorsed college where everything has to be ok with the Vatican and thus attracts a very specific group of American students? If so, then it’s the best location with decent academics. (Food isn’t great but you have lots of options nearby).
Key questions will be
1° Do you want Catholic colleges, Protestant Mainstream colleges, or Protestant Evangelical colleges?
(Note that Evangelical colleges would be considered “dry” and thus would have few parties since drinking alcohol could be bounds for expulsion. In addition, there’ll be mandatory chapel/religion class).
2° Would you rather attend a secular university?
I actually know most of those 
but it’s true they’re all very small. Are there any others you might have left off?
For the full-on American college experience with excellent academics, Centre College has what you want - parties and Greek Life, excellence with international students, small classes with engaged students. It’d be totally different from what you know. You’ll have to plan your travels. The weather is better than most other universities. Secular.
Coe is a good college in a nice town, lots of things to do on location, good academics. Non religious.
Virginia Wesleyan has an excellent coastal location (Virginia Beach). However it is very small, not sure it’d suit your academic needs.
Nebraska Wesleyan is in a big city but that big city is far away from most places visitors want to see.
Yes. I was thinking Clark. Not Clarke. Thanks for clearing this up. @retiredfarmer
But Clarke might be nice too.
Thanks everyone. Catholic U does look really good but although I don’t care, most of my family are protestant so i dont know if that will work out. Centre college seems to get a lot of mentions so I might go for that. Ill check out coe, u of saint thomas and a few others mentioned.
I think that Coe College in Cedar Rapids, Iowa is very close to Iowa City & the University of Iowa.
The University of Iowa has about 28,000 students & should offer all the entertainment that you are seeking.
Yes, Coe is about 30mn to Iowa City. From there, you can easily go to Chicago and the Twin Cities, two major US metropolis.
Attending Catholic U of America would be strange as a Protestant. I guess it could be educational since the context is very different from Northern Ireland’s, but it’s probably as Catholic as you can get in the US.
@scorpion1129 , other than the college itself, do you have any preferences about location? I just want to emphasize that most people from the UK find it difficult to comprehend how really big the US is. Being in the “middle of nowhere” in the US is vastly - vastly - different from being in the “middle of nowhere” in the UK. Make sure to include research on travel options, times and distances to places you may want to visit, as part of looking at the various schools.
Yes, understand that in most parts of the country you travel (in equivalent) from Bath to Bournemouth to find ONE city, or perhaps from County Antrim to Dublin (?). You can commonly drive five hours and still be in the same state. There aren’t many trains, although there are buses - check out Megabus for instance. There are trains along the east coast, which is why people have been recommending CUA, but I really don’t know what it’d be like to attend CUA as a Protestant. Also important, the concept of college towns - these are towns centered around a university, therefore walkable and designed with students’ needs in mind. Cedar Rapids (and, to a much lesser extent, Iowa City - Iowa City exists on its own although it has a large percentage of students) would be excellent examples of these.
Will you be 21?
How serious is your interest in business? Are you obligated to study that because of your scholarship? Do you need to be able to use any of the credits you earn in the US to apply them to your degree program in the UK?
If you don’t need to be able to use the credits for anything, and you aren’t obligated to study anything in particular, then this year can be just random classes you are curious about. In that case, you do want to examine the specific course offerings. For example, both Monmouth and Shenandoah are known regionally for their theater programs, but at Shenandoah theater is a conservatory program and it would be difficult to enroll in those classes or to participate in any productions.
If you are interested in focusing on business, then you can compare your list with the list of collegs and universities with AACSB accredited business programs at aacsb.edu
Some of these colleges and universities have websites that are difficult to navigate. That might be a good criteria to consider too. 
Lastly, don’t neglect to consider weather. You might need a whole new winter wardrobe!
Well, if you scratch Catholic U because of Catholicism, then UST would be equally off the table. (Unless you have a clear preference between majority-white Catholicism and majority-Latinx Catholicism…)
On the one hand, most of your peers at either of these schools would be Catholic. On the other hand, you would’t have to worry about the school’s graduation requirements, so it may well be that you wouldn’t have to take any religiously-oriented classes if you didn’t want to. Only you can determine whether the Catholic context would be an issue for you.
To me, this reads like a choice between a relatively self-contained residential LAC campus experience (Centre or Coe) or a smaller urban university in a cool location, with a business school, that happens to have a Catholic frame of reference (Catholic or UST). Coe strikes a balance because it is in a small city, but nobody would mistake Cedar Rapids for Washington DC or Houston. It really depends on your priorities and where you think you’d feel comfortable. (But with those four schools setting the bar, I still don’t see another obvious contender on the larger list.)
Agree with the overview provided by @aquapt. Catholic and UST offer the most interesting urban locations. If you want an interesting, more urban location these are likely your best options. Other schools will offer a more rural LAC experience.
Coe and Centre are solid. The other school I may suggest to look at is Shendandoah. I teach at James Madison… about 1 hour south of Shenandoah… and, while the Shenandoah campus is relatively small, Winchester is a cute town, only about 1 hour south of Washington DC.
UST in Houston? This uni is small at 3000 and again with the catholic. And Houston with no transport, little money and ? too young to drink, might have little to offer. No way will this be a US college experience. The trendy Montrose nightlife requires serious money and an ID.
Southwestern is in Georgetown here just outside of Austin, TX. Come have some BBQ and enjoy some live music festivals.