Ok, this might be a bit rambling because I haven’t had enough coffee yet, and your situation is one of the more tricky ones. Please bear with me and I hope some of this might prove useful to you in terms of clarifying your thinking.
You have a lot of outstanding academic credentials, but your financial constraints are going to narrow the field significantly. The essential problem is that the majority of the schools that would be the best fit for you academically are also largely the schools which tend to make most or all of their aid need based, and so aren’t going to be affordable to you. That leaves you in a position where you may be forced to compromise somewhat in terms of academic rigor or prestige by dropping down the rankings to find a school that will meet your financial criteria (either through lower cost or more likely large merit awards), without ending up at a place where you are going to be unhappy because the academics aren’t challenging.
Honestly, the University of Michigan sets a pretty high benchmark that is hard to beat for your situation - not saying it can’t be done, but the combination of in-state affordability and academic rigor and prestige is tailor made for you. However, you don’t seem very excited about it, and that is a very important consideration as well. I do think you definitely should look into it more - maybe you will find it is a better match than you initially thought. Or perhaps you will still not be interested, but you will have a better idea of exactly WHY it doesn’t appeal to you (the size, the social atmosphere, maybe you just really want to get out of Michigan, whatever.)
There are definitely alternatives - @whenhen listed some pretty good ones above. Case Western definitely popped into my head, given your need for merit aid and the majors you are considering. Finding these types of “thread the needle” type schools isn’t that easy though and I think you can help yourself out a lot by thinking a little harder about some of your criteria - up above, in response to my questions, you sort of hand waved my questions about school size preference and the urban/rural thing. Your geographical preferences are also a little vague. The problem, for me or anyone else who wants to give you some suggestions, is that you haven’t really narrowed the search space enough for anyone to be able to give you a manageable list that you are going to be able to research carefully. I think your best move is to try to get a little more specific on some of these issues if you can - it might take some campus visits to clarify your thinking, but there are some things you can probably do just by thinking a little more about them.
Here’s a couple of examples:
School size: You expressed no preference. Here’s my take on that.
First of all, you have a range of majors you feel are appealing to you (math, stats, physics, comp sci) - that’s a good range of stuff you might end up in, and it makes sense that you should pick colleges that cover ALL of those pretty well, so you won’t get caught having to transfer when it comes time to choose. My personal take on that is that it definitely should eliminate most schools below a certain size, because some of those majors either won’t be available at all or might be very tiny departments that are going to feel restrictive. (Yes, there are some very small schools that do specialize in STEM, but as a general rule this can be an important issue with smaller schools.) So, I think that you should consider just crossing off most schools below about 3000 students, because they won’t have the options for you.
Secondly, your comments about wanting to avoid the frat / party scene and feeling that you are somewhat social awkward should be explored a bit further to see if you can’t draw a few more lines. At a very small school, some people find it social oppressive because everyone knows everyone else - some people like to be able to get lost in the crowd a bit or maybe they want a bigger pool so there are enough people that they can find a sub-culture / niche / clique they are comfortable with. Alternatively, some people like that small community feeling - they don’t want to feel that they are just a face in the crowd. This is something you need to think about a little more and see if you don’t really have more of a preference than you have expressed so far.
(Quick note on the socially awkward thing - lots of kids feel that way in high school, and then it fades away with astonishing speed in college. For others, it remains an issue…you really need to think about it a bit, and try to imagine what kind of environment is most likely to make you feel comfortable and like you fit in.)
Geography:
I think you are a little vague on this. You mentioned you’d prefer somewhere “warmer” - what exactly does that mean? Warmer than Michigan? Or “Shorts in January?” Another thing to consider is how far away from home is your limit? You mentioned the east coast, so obviously you are fine with being relatively far from home, but are there limits? I really suggest you sit down with a map or a list of the 50 states, and cross off the ones that just aren’t worth considering.
Urban / Rural:
You said this doesn’t matter to you - maybe that really is the case, but I think you should consider it a bit more. So much of you life / EC activities has revolved around horses and 4H. Given your self-described “social awkwardness,” you do really need to consider if you might find the adjustment to college easier if there were good opportunities to maintain some contact with these activities that have been such a big part of your life. Maybe that doesn’t seem important to you right now, and maybe it REALLY isn’t important, but I think that’s something you really need to consider carefully. Certain schools are going to make these kinds of activities very convenient and available to you, and some are most definitely not.
Anyway, I hope you find some of this at least a little bit helpful.