To me a liberal arts college is a smaller school that focuses primarily on undergraduate education. There are quite a few that are public.
One example is the Massachusetts College of Liberal Arts. I honestly do not know whether it will fit your 50-60k / year budget out of state but it would surprise me if it doesn’t. If you are in state (which seems possible given your screen name) then it should be way under budget.
UVM (Vermont) is a bit larger but is still not a huge school (perhaps 12,000 undergrads). The full cost out of state would be over your budget, but they do have quite good merit scholarships possible for out of state students. The last time that we checked (quite a few years ago) the NPC did predict merit aid, and for us was spot on accurate. U.Maine is another relatively small public university (8,000 undergrads) that can be relatively affordable for an out of state student.
While Canada does not use the term “liberal arts college”, they do have some smaller universities that focus primarily on undergraduate education. As some examples in eastern Canada, you might look at Acadia, Bishop’s, Mount Allison, and St Francis Xavier. All are relatively small schools that focus primarily on undergraduate education, although some have a few graduate degrees (such as master’s degrees). UNB and U.PEI are also smaller schools, although I will admit that I think of U.PEI mostly for having a superb DVM program which is of course very much a graduate program. The last time that I looked most of these would fit your US$50k-60k per year goal even for an international student without aid (I have not looked recently, keep the exchange rate in mind).
I agree with others to set a budget and stick with this. We did this.
We had a similar experience. One daughter got into NEU and BU but both would have been full pay and way over budget. We said no. She went elsewhere (UVM, with good merit aid), did very well, loved in, and then switched to a major that NEU and BU don’t have (something about a lack of cows and horses on campus in downtown Boston – we got lucky). Then she graduated and thanked me for not letting her take on debt for her bachelor’s degree. At the age of 22 when on the first job a former student’s perspective may be different than when they are 18 and graduating from high school.