Are there any good colleges with no language requirements for admission from high school?
What is the reason you didn’t take a foreign language? I know several kids who did not take language due to learning disabilities (dyslexia), who are now at very selective LACs, including a NESCAC and another ranked in the top 15. But they got good support from the guidance counselor who helped provide documentation and reccos.
How are you graduating from high school without a foreign language? Were you homeschooled? Did you decide to skip world languages thinking it wouldn’t matter and just realized it is one of five core courses to get into college?
If you’re a rising senior, you can still cut your losses by finding a community college nearby and taking two semesters of whatever language is offered at the least inconvenient time. Two semesters of college language will meet “3 years of high school language” which covers almost all universities except the most selective.
Even homeschooled kids can take a foreign language. Many states have virtual online schools, which include foreign language classes.
You need to provide some more information to get useful responses. Are you a rising senior? Do you have zero foreign language credits? Do you have a documented learning disability that prevented you from successfully taking a foreign language? What’s your intended field of study, home state, desired location? You asked about “good” schools that don’t require a foreign language. Most competitive schools require two or more years of the same language, and the most competitive expect 3 or even 4.
I found this old list from 9 years ago of colleges that supposedly don’t require a foreign language, but obviously you shouldn’t consider it reliable or up to date. http://collegelists.pbworks.com/w/page/16119454/Foreign%20Language%20Not%20Required. But you could look at the list and if any sound like ones that would interest you, go to that college’s website and check their current requirements.
In my home state of Arizona, the state universities require two years of the same foreign language as one of a list of “core competencies.” Example ASU: https://students.asu.edu/admission/competencies. But the website also says: “Admission may be granted with one deficiency in no more than two competency areas. Deficiencies in both math and laboratory science are not acceptable.” I’m unclear on whether having zero foreign language counts as one deficiency or two deficiencies. You really need to talk to your guidance counselor.
As others have noted if you have a valid reason for not taking a foreign language such as a being dyslexic then it should be fine. If you just chose not to take foreign language in HS then you would need to research the HS course requirements of schools you are interested in (there is no shortcut).
It’s highly advised that you take a foreign language- particularly a popular one (I don’t mean to dissuade you from independently selecting a language which interests or has cultural/ancestral significance to you, I’m simply being honest.) That said, languages which look good to colleges, but aren’t the most difficult to master for a native English speaker, include German, Spanish, and Portuguese. Though you may think “Oh, everyone takes Spanish”, while there’s truth that many choose Spanish as an alternative language, it looks much better than taking a language which has no real use outside of specific situations or in its native country. Aside from this, obviously, Mandarin Chinese and Arabic are excellent languages to uptake.
With that, I encourage you to take some form of language if it isn’t already too late for you. Colleges love to see an alternate language aside from English (or your native tongue). Shows you’re diverse in your education, interests, and skill set. 
In choosing a FL to take in college or HS, a student should choose a language that will be useful to him/her, whether for travel, graduate studies, etc.
A student should never choose a FL (or any other course or EC) for the purpose of “looking better” to colleges. They won’t care what language you study.
Right, there are no secret special languages, lol.
In fact, some kids do their 2-4 years in Latin, which is certainly not an everyday language, outside scholarship.
@lookingforward Getting off-topic a bit, but might have missed the post a few years ago form the student who wanted to know if the college would accept Klingon as his foreign language. 
Forgot that, wonder how far he got.
There are a lot of colleges that will accept ASL in fulfillment of the FL requirement, including quite a few competitive colleges. https://www.mlschools.org/Page/3128.
@skieurope “I don’t mean to dissuade you from independently selecting a language which interests or has cultural/ancestral significance to you, I’m simply being honest.” - My original post
I completely understand this. But the OP has to also take into consideration the gravity of his choice of Alternative Language. Depending on their major, a specific language could look better; or a plentitude of languages would have greater weight over being multilingual in application for another major. Certainly, Arabic is more eye catching and seen as more practical than Italian.
That said, OP should stick to what appeals to him. Depending on his major, a foreign language could have little to no effect on his acceptance over someone else, depending on his GPA, test scores, or extracurriculars. But you cannot argue that in the modern day market, Mandarin is in far higher demand as a second language than Vietnamese, no? Thus seen as more practical and to improve ones’ appearance on an application?
Most colleges would not look highly on an app without a second language, independently taken or through a school elective. OP may choose whatever he likes, I’m simply looking at it from a far more practical point of view.
@Corinthian thanks for that! My daughter is taking ASL at her school but they said not all colleges accept it. Good to know!
Most selective 4-year colleges would not look at an application without foreign language learning (unless there was a specific, official note about a learning disability).
The reality is, however, that for many US HS students, the options for foreign language study is Spanish or … Spanish.
One can argue whether one particular foreign language is more practical than any other, but while many espouse the flavor-of-the-week languages like Mandarin and Arabic, the number of HS’s that offer either of these languages is few and far between.
So I just go back to what I said before: a student should make the choice based upon his interests. The college is not going to care what language he selects. If an applicant from the Punahou School, for example, presents an exceptional application package, no AO is going to say, “Darn, I would have admitted him if only he didn’t choose to spend 4 years studying a useless language like Hawaiian.” YMMV.
We’re all assuming that the OP is a student, but maybe that’s not the case. Maybe the OP is a parent/relative/friend who just wants an answer. My younger D hated her French class freshman year. She wanted to skip taking a FL since it’s not required for graduation in our school district and she has some relatively mild dyslexia. But I persuaded her after many tears and arguments that she needed to take some FL or ASL for at least 2 years. She settled on Latin which she takes online and has found easier to manage. Still it has been a struggle (not yet finished) to get her to complete 2 years worth. But it was easier to persuade her once I showed her how much it would limit her options not to do at least 2 years.
It is possible that a heritage speaker of Spanish may already be more advanced than the Spanish courses at an under-resourced school where Spanish is the only offered foreign language, so there is no point for him/her to take any Spanish courses there. But then at least s/he could take the AP and SAT subject tests in Spanish to prove that to colleges.
Anecdote: In my long-ago high school Spanish I class, two students failed (not “failed” as CC students sometimes use it, meaning a C - I mean they got grades of F). Both were born in Mexico and spoke Spanish as a first language. They didn’t think they had to study (not speculation, they told me this); they thought it would be an easy A.
Think of all the US-born, English speaking American kids who fail English every single year.