So if it were me, assuming that you get admitted to that state university, I would not be looking for OOS public research university options. I’d be thinking about how to get competitive options that would be more different from that sort of experience.
I get the interest in Rice from that perspective–they really make the most of doing things their own way.
In terms of other research universities like that, people in my circles with your sorts of interests often cross-shop Rice with at least WashU and Emory. If Rice is easily your favorite and you don’t consider those as better options than your state university, that is fine too. But to me they are the most obvious “If you like Rice . . .” sort of answer.
A less obvious answer but one I would personally strongly consider is going to a Liberal Arts and Science College instead. I understand you are concerned about family and peer pressure, and such people can sometimes not really understand the LAC scene, but these can be great schools for premeds. Great undergrad teaching in relevant departments, great advising, plenty of undergrad research opportunities, maybe a bit less of a sense of internal competition . . . .
And in some sense, what makes Rice special among research universities is they are sort of trying to reduplicate some of the aspects of an LAC-type experience. But . . . why not go for the real thing!
OK, so normally this is not where I would start an LAC exploration, but since you may need to sell yourself, your parents, peers, and so on, you can check out this list of feeders to med schools, particularly the first list which is per capita:
A lot of what I would call “the usual suspects” from the top research universities, and Rice is at #4. So, yeah, that’s a real thing for Rice. There is always a very legitimate question of value-added versus self-selection, but at least we know Rice is among the colleges where lots of students end up admitted to med schools. WashU is #10, Emory #17, so yeah, with the same caveats.
But there are actually quite a few LACs doing really well too. In the top 20, you have Amherst #9, Haverford #11, Pomona #12, Swarthmore #14. Of course these are not exactly easy admits themselves, and Amherst, Pomona, and Swarthmore would be considered by many absolute top tier LACs. But Haverford is a little more interesting in the sense it is a sort of Rice of LACs if you will–a very academicky college that is proud of having its own distinct culture. Could be worth checking out.
OK, then you have Wellesley at #22 (top tier women’s college), Williams #25 (another absolute top), Barnard #26 (another top women’s college), and Grinnell #29. Grinnell I am going to focus on because again it is a very academicky college with its own vibe. Notoriously in the middle of a cornfield, but as a premed? Could be great.
OK, so I’ll stop listing every LAC, but here is the thing. You don’t even get to Michigan, UCLA, and Cal until 53-55. Again, there is a LOT of self-selection behind that, but still, this leaves lots of room for alternatives. For example, I think Wesleyan (#36) and Vassar (#43). are both great LACs well worth considering, Bryn Mawr (#41) if you are not male, Oberlin and Carleton not far behind the top publics, and many more.
OK, still not convinced? They also do a “top” medical schools version, which I don’t see as a big improvement, but it does bump up the top publics. Still, the LACs I mentioned above are either still above or at least not much behind the top publics.
And this isn’t just me. They pick up on the same pattern, and actually do an LAC-specific list.
Anyway, that’s my pitch. Rice is great, but if you want more options to consider as true alternatives to big publics, I think LACs are a great place to look.