Can you manage to visit them, if you haven’t already?
If you can’t, have you read Fiske and the Columbia and Brown threads here?
FWIW, my husband, born and bred in NYC and something of an extremist on the pro-NYC front, only considered schools in NYC. He went to Columbia. He’ll tell you he was satisfied with his choice because he got to stay in NYC. . . BUT he didn’t really enjoy college. Columbia wasn’t a particularly good fit for him, aside from being in NYC. He didn’t warm up to the people much and he had mixed feelings about the Common Core (it was a great education, but he would have liked the flexibility to take some classes he was interested in but didn’t have time for.)
My advice to you, based on the little I know about you, would be to go to Brown. Providence certainly isn’t NYC, but it’s not the middle of nowhere. You have a lifetime, plus school vacations (I’m assuming you live near NYC) to see Broadway shows. I promise, the difference in prestige between Columbia and Brown is negligible and is not going to have a significant effect on the course of your career. If you’d actually enjoy the people, the atmosphere and the education at Brown more, Broadway and prestige aren’t enough of a reason to choose Columbia.