Yeah, I have a different approach - more similar to @monydad’s. The prestige or reputation of your exchange school doesn’t really matter that much, unless you were planning to come to the U.S. to work (and even then, it wouldn’t matter much - you’re only spending a semester there). Really, the focus of an exchange should be on the experience that you get there. So I’d pick either based on the campus experience or the location of the university - and just like he says, I’d either pick something in a large city and/or a travel hub that I could easily see more of the U.S. from, OR something that was indicative of the traditional big flagship university experience.
Big city schools would include Baruch, Bentley, Boston College, Boston University, Belmont, Brandeis, Columbia, NYU, Emory, George Washington, Georgetown, Georgia State, Northwestern, Tulane, UCLA, Southern Methodist, UPenn, USC, University of Minnesota, University of Maryland, UT-Austin, and UW-Seattle. There are some smaller cities represented there, too, like Richmond (University of Richmond), Madison (Wisconsin) and NC State (Raleigh). The Northeastern cities - Boston, New York, Philadelphia, and Washington D.C. - are connected by a pretty extensive travel network that runs from Boston to DC. Visiting other cities from the Southern cities (New Orleans, Nashville, Atlanta, Austin) is difficult - the South is pretty spread out. Chicago, too, doesn’t have a whole bunch of cities nearby it.
If you wanted to be in Boston, I’d pick Boston College, Boston University or Brandeis over Bentley. If you wanted to be in Atlanta, I’d pick Emory over Georgia State (GSU is very much a commuter-style school).
Or you could go to a large public flagship university. University of Minnesota, Oregon, Indiana University, Purdue, University of Wisconsin-Madison, UW-Seattle, Texas A&M, Ohio State, NC State, UNC-Chapel Hill, University of Maryland, and University of Michigan would give you that kind of experience. Arizona State may kind of.
Minnesota, Maryland, Wisconsin and Washington are four universities that have the benefit of both being in or near large (ish, in the case of Madison) cities and giving you that large public university experience. Out of the four, honestly, I might go with University of Maryland. You’d be right near DC, so you’d get to see that city; it’s a large university with participation in sports and the whole nine; and DC is a travel hub. In a couple of hours you could see lots of East Coast cities.
University of Hawaii would be an interesting tropical experience, but it’s expensive to travel to the mainland U.S. from Hawaii so you couldn’t really travel much.
Willamette is a small liberal arts college in a smallish city on the West Coast. It and the University of Richmond are the only two small liberal arts colleges on the list. That’s a unique kind of experience, too.
If it were me, I’d prioritize being on the East Coast where you could travel and see lots of U.S. cities during your time, as well as being in a large city where you can take advantage of all the amenities the city has to offer. But I’d also want to be on a kind of traditional college campus. So my list would probably look something like Boston College, Columbia, Georgetown and Maryland (not necessarily in that order). Penn is a very close fifth choice, but I think Boston and New York and DC are better cities and easier to get around in using public transit than Philadelphia.
If I wanted to do big public flagship, I’d probably list Maryland, Michigan, UNC-Chapel Hill as my top three choices. The fourth one would be either Wisconsin, Washington, or Minnesota depending on what kind of experience you want to have.
