Your high stats can help potentially get you with a high merit award. However many of the smaller colleges want to have their best offers got to the students who indicate the school is one of their top picks (see the article and list of 20 best colleges for merit aid, Money Magazine, Jan/Feb 2015). Looking down that list and looking at the schools on-line, you can see if any are a ‘fit’ for you. The list of 20 is culled out of the 665 schools that are in Best Colleges ranking. Article also discusses where your grades and test scores put you in the top quartile of the applicant pool.
The benefit of going to a smaller private is you could fit many areas of interest (more flexibility IMO). However if you have a larger university with an excellent international relations/studies dept, that may be a better fit.
You also have to consider the difference in cost (so cost benefit) of a higher priced school. If your parents are willing to help pay the difference between a generous Ivy, only apply to the ones that are strong in the programs you are looking for or the ones you have a best chance of admission.
Are you thinking about graduate school? You may want to pay less out-of-pocket for UG. Also look at those graduate programs and see what kind of preparation you want in UG.
Some schools may have great career-building internships in your field.
There are some flagship public universities that are exceptions on higher merit for OOS (as article says, Alabama, North Dakota, South Carolina). UA has an excellent honors program - you will have to decide if they offer enough in your field of study, but they offer a lot of diverse education and there are a lot of high stat kids on campus (they have the most NMS of any public university, and I believe are ranked #4 behind 3 privates). UA has a special package for NMS which adds a 5th year of education. My dau is a student there (freshman with presidential and a few other scholarships).
My advice would be to research the advice on this thread, make sure you have looked at the smaller schools that offer what you are looking for and may have enough merit for you to attend. I agree with the magazine advice: if you are interested in a school, make sure they know it because some will not make a high-aid award to students they believe won’t probably choose their institution.
The more you have researched and pared down, the better for the application process. You want to put your best foot forward to your top choices at the get-go on the application process. If a school will not fit the budget, use your energy to the ones that will.