BU is not an option. Forget it. Last cycle, they waitlisted about 5,000 students and admitted 3. Yes, 3.
The options are Vassar or Hamilton. Both schools have high freshman retention rates, meaning students return for their second year. Both of these schools are going to have a lot of campus clubs and activities to keep students busy on campus. There is no need to get to the city on a regular basis and in fact, students will stay on campus the majority of the time. That is where their food, bed, and friends are.
Vassar is not particularly convenient to NYC, but it’s very doable. Hamilton is much less so. Hamilton is probably slightly more academic in feel, but both are going going to be very rigorous. Vassar is definitely more arty and creative in feel. Hamilton is a bit more mainstream. Both are beautiful. If your child is an arty, creative type of person, Vassar is probably a better choice.