Tufts immediately came to mind for me as well. Their program with NEC creates great opportunities for their students.
Bard could be worth a look. Not exactly near a city, but it could be a fit and has access, if not proximity, to NYC.
I have known two very serious classical musicans who chose Haverford. I know very little about the music program there, but I suspect the vibrant music scene (including Curtis) in Philadelphia was an attraction in addition to what the school might have offered. That one, if the piano program works, should hit all the criteria.