If you’re open to considering the Midwest, you might want to put Macalester (Twin Cities), Carleton (Northfield, MN), St. Olaf (Northfield, MN), and Grinnell (cornfields of Iowa) on the list. All amazing schools.
Based on the “vibe” you think would work best for you daughter, I’m guessing Colgate wouldn’t be a great fit.
As mentioned to you already, given her stats and her interests, she might want to consider Barnard College at Columbia University:
https://neuroscience.barnard.edu/nsb-major
On one hand, it is a small, elite, liberal arts college with the feel of a “sisterhood”. On the other hand, it is fully integrated into the large Columbia University, in New York City, with all the opportunities that offers.
Classes, facilities, libraries, dining halls, faculty etc. are co-ed and shared with/by all Columbia students – so not at all a “cocoon”. However the women-only dorms can offer a welcome retreat whenever sought, or while still adjusting. 2nd year students have the choice of living in neighborhood apartment buildings to fully immerse in “city life”.
Of course only you and your daughter can gauge, whether living in NYC would be a welcome challenge to grow out of her shell, or something completely out of the question.
She might consider Honors Programs at large research universities and at least visit a couple to check them out. Many programs include special housing and a tight knit social scene plus research perks not usually granted to undergraduates. I understand the appeal of a small LAC campus, but academically they can’t compete in breadth and depth of classes offered. Also, a large university will have more of everything else to choose from in terms of clubs, interests and friend groups. My sample size of two insight is that friend groups freshman year generally are made on your dorm floor. She sounds like a perfectly nerdy Honors kid who will want to avoid the worst excesses of the traditional Frosh dorm experience.
I’d add Wooster to this Ohio list, which has become a haven for this kind of student and merit abounds. And the Independent Study program would more than scratch that research itch.
So many great suggestions. All I will say is Facebook the schools. She will find her peeps. She will be fine.
If Ohio is in play, Oberlin is “meets need” and generous. It has a special vibe with a completely integrated small town and campus and live music performances every day, plus smart, talented, quirky kids, but it’s fewer than 3,000 students and that’s including the Conservatory.
UChicago, Swarthmore, MIT, Kenyon, William&Mary.
If you’re willing to size up and move west, the U. of Washington has a very dark academia vibe (personal experience). Very cool place to study with very smart (nerdy?) people and a stem-heavy focus.
If your daughter wants to get a small-class experience there, she can apply for the honors program. She could probably get in with those stats.
I agree with the suggestion above but want to reiterate Brown. Yes it’s a reach but she has a shot. Brown has the vibe she might like, similar to a LAC, freedom to choose classes, but big enough with great STEM.
Amherst (along with Smith) is part of a consortium with 4 other schools and also has freedom to choose classes.
Is she especially interested in women’s colleges?
URochester was my first thought too.
Case Western Reserve U might also appeal. It’s also a mid-sized research university, with fewer than 6000 undergrads. CWRU is 25% Greek, which means that one can have a great quality of life there without getting involved in Greek life at all… but also, it’s a very nerd-friendly Greek system, and a sorority might end up giving her some of the same benefits that she’s seeing in women’s colleges. Either way, the vibe of the school and its strong research piece could make it a good fit.
What about Connecticut College or Bates?
Just came here to say that Colgate, F&M, Lehigh, Bucknell, and Lafayette don’t seem to me like good fits for a nerdy, introverted student who is fearful about fitting in. These schools are very Greek-oriented, with the attendant partying. Especially F&M, Lehigh, and Bucknell.
For her personality, I’d highly recommend a school that has some variation of a house system or residential college system or options. These include Bowdoin, Williams, Harvard, Rice, and Yale, Vanderbilt, Dartmouth, and I believe Middlebury. (Actually, I believe F&M has this too.)
Other suggestions to look into:
Scripps College (not in northeast, but if she likes women’s colleges it’s worth looking into)
Washington University
If she can get in, I think she would like Wellesley or Bowdoin.
One hidden gem we found (and where I have a kid) is at UCSC. He is also an introvert and nerdy. He selected it bc they are strong in his area if study, but they also have a residential college system, each with their own personalities. He selected a quieter/introverted one (Crown/Merrill) and it’s been a good fit. Part of that is also the room he ended up in and housing is a serious issue in Santa Cruz. Also it’s a stunningly beautiful setting with lots of hiking, cute wildlife, beaches, trails and redwoods right on campus, which I think also help nerdy introverts feel a little more at peace. If you have the means to support your nerdy introvert in case on campus housing doesn’t quite work out (there are some hextuples, but I don’t think they would put someone who wants a quiet living situation in that kind of room) it could be an option if they have what your kid wants to study.
At a high level, I second most of the suggestions in the thread that were responsive to what you said she wants (and not what you didn’t describe she wants). I also agree, again at a high level, that schools like Colgate, Lehigh, Lafayette and Bucknell seem like non-fits with the others, though we know personally a variety of kids who are fairly described as introverted who have thrived at those schools, two recently at Bucknell. These are kids who were bit sheltered, quite shy/introverted and didn’t profile at all for the school spirit and party scene, or as ambitious and confident pre-professional types, and were nowhere near a fit for big Greek.
Full disclosure, when I hear “introverted,” I also tend to think “awkward” or “quirky”, which may not be accurate for you, so keep that in mind. From my travels among the very many fine LACs in New England, NY and PA (because you said she wanted small in these general areas), I surmise that a fine physics education is to be found at a number of them, and probably all of them. But that’s not very helpful.
However, if I’m looking for (1) small, (2) fit for quirky, (3) solid physics and (4) research, I land on Williams, Wesleyan, Wellesley, Vassar and BMC, with my unmitigated bias for Wesleyan duly noted. I omitted Hamilton, which is also high level in physics, because there seems to be a common view here (I myself really don’t know) that Hamilton profiles a bit more like a Colgate or a Bucknell. Someone will jump in here on that point, I’m sure.
Wesleyan and BMC are especially good candidates to consider because they really are places where all kinds of people fit in, because those two schools lead the LAC category (with Wellesley a close third) in research spending and, lastly, because both schools have graduate programs in physics, thereby adding course depth and some of the other goodies that come with educating graduate students, while still checking the “small” box.
Again, I’m not opining on any of the schools suggested thus far that don’t fit the criteria you set out, other than to say that most of the description offered of the University of Washington, a school I know very well, doesn’t jibe with my impressions at all. If she’s willing to go bigger, then a lot of other places, including those mentioned, could work well. Brown, for example, would IMO be a fine place for a kid who is introverted or quirky, even though there seem to be plenty of enthusiastic extroverts on campus as well.
This professor, who taught at Colgate before joining Hamilton’s faculty, offered an unprompted opinion regarding how different from each other the two schools appear to him:
Meet the New Faculty: Darren Strash, Computer Science - News - Hamilton College.
Regarding Hamilton’s physics department, one of its professors was recognized recently by the American Physical Society through its annual award for research and mentoring at a primarily undergraduate institution. For insight into Hamilton’s physics community, these articles may be of interest to the OP:
Teacher, Mentor, Researcher, Friend: Alumni Praise Professor Gordon Jones - News - Hamilton College.
Be careful with NPCs; some of them are more accurate than others. For what it’s worth, I was at Lehigh for a math event just this spring. There seemed to be a significant nerd contingent there.
So I’ll throw out two schools that don’t have the dark acedemic vibe but might net her great aid and have very good STEM and the nerdy vibe and interesting/flexible curricula: RPI and WPI.
RPI has lots of cross over majors and research and the top companies hire out of there. My son got very substantial merit offers for applying to the sciences (bio/chem) when his engineer friends didnt even get in.
WPI has a publicly-stated goal of recruiting more women to STEM and we saw merit awards in the $25k range for comparable female students to yours. They also have very flexible curricula. Take a visit to WPI - it tends to move up the list.
They are not Vassar or Wellesley or Colgate or Bowdoin or Smith. But they can make a great deal of financial sense.
I sent you a DM. Take a look at the “R” icon at the top right of your screen and then click it.
I would second another look at Wooster and St Olaf for a nerdy introvert future science major 
- bonus: pretty laid back atmosphere.
Also Grinnell but much more selective.