So I had my heart set on NYU, then Gtown screwed me over by accepting me off waitlist. I am in love with both. I have a couple questions:
DUDE, NYU all the way!!! Give up your spot on the waitlist. 
jk
Seriously, though, I think it sounds like you are unsure of what you want to do in life in general as pre-med and pre-law are two very different tracts. Frankly, I was a little surprised that with your affinity for the piano that you were so intent on leaving NYU as New York would provide some excellent opportunities to continue that interest both in playing and in hearing some world class talents.
I think economics would be a draw. NYU would provide better economics training in econometrics while GT better for international economics.
I think the two schools are very different. While Georgetown is in DC, I don’t think of it as an urban school in the same sense as NYU (the ultimate urban university, IMHO).
I say go to the one that you think will cultivate your passions. My guess, from what you have shared with us in other posts, is that you are the kind of person that needs to feel passionate about something to really get energized by it and excel.
I am waitlisted for economics, though, so take the above with a grain of salt. No one had responded and I know you are on a time deadline so I thought I would contribute but I don’t want to be biased.
@pianogeek Care to tell us what you chose?
@TyedTyper thanks so much for your comment! It was very detailed and I’m surprised that you caught my work ethic through my CC interactions. I haven’t checked my threads in a while so sorry for not replying. I will be sending in a deposit to Georgetown tonight and withdrawing from NYU. Best of luck to you on the waitlist!