Students from Brown get great jobs, get into great graduate programs, and have great lives, too. Providence is definitely not NYC but it has some good theater, great food, and is a very livable city. That said, you will definitely have a greater variety of options for internships during the year at Columbia, especially if you want to go to Wall Street. And if NYC is your end all and be all, then go for Columbia. (I think they are both amazing schools.)
The most important thing: choose the school that is the best fit for YOU. Simply choosing a school by the rankings is a recipe for disaster. Being miserable at a school with a higher ranking is a terrible way to spend four years.