Has your daughter looked into East Carolina’s neuroscience program https://neuroscience.ecu.edu/? Also, even if a college does not have a formal degree called neuroscience, your daughter can essentially still take the same courses from biology, psychology, etc, to study what she wants (and many universities allow students to create their own individualized majors). Also, honors colleges can help make a bigger school seem smaller and surround students with more academically-inclined peers.
Is the $30k budget considering what would be able to happen with 2 or 3 kids in college? Or just one?
To give a sense of distance, I’ve calculated the times from Greensboro, NC which seems a midway point between RTP and Charlotte, as a very competitive NC high school is probably in one of the two metros. Below are some schools that are within a 7ish hour drive that would have a decent chance of meeting your budget via merit aid (though definitely not extremely likely chance) and might have the intellectual environment your daughter is seeking. If you get need-based aid on top, that’d be even better, but we’ll wait to hear the results from the NPCs.
Smaller Schools
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Agnes Scott (GA): Women’s college of about 1100 undergrads and part of the Atlanta consortium whereby she could take classes at other colleges like Emory, Georgia Tech, and Spelman. 5h6m
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Centre (KY): About 1300 undergrads, 6h43m
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College of Wooster (OH): About 2k undergrads, 7h13m
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Furman (SC): About 2300 undergrads, 2h58m
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Muhlenberg (PA ): About 2100 undergrads, 7h33m
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U. of the South (TN): About 1700 undergrads, 7h4m
Larger Schools (look for the honors programs)
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U. of Kentucky: About 22k undergrads, 6h48m
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West Virginia. About 20k undergrads, 5h57m