There are bike shops in the city that will rent you racing bikes, I believe it's like $50 a day.

Where do your parents live?

A local parking garage might "park" your bike for you for a couple of bucks. A superintendent of your parents or a local building might find a spot to put your bike for a couple of dollars. Put an ad on craig's list. I'd let you keep your bike at my house, but I'm in Long Island. Maybe someone will let you keep your bike at their place.