A.H.
Why don't you try to priceline a hotel? In NYC you can pick very specific neighborhoods to bid in and if you pick 4 stars or whatever you won't be disappointed. My husband and I have stayed at REALLY nice manhattan hotels doing that. In a lot of cases you'd be able to park a car at the hotel of course, but that could be really expensive. (I mean, all of the parking is expensive, but I mean crazy) We always parked (moved away last yr.) at the park n lock lot on 42nd st. between 9th and 10th ave's. Its cheaper and it nice that its park and lock so you don't have to wait for the valet or go down some crazy basement. There is of course a subway station in like 1 blk. to take you wherever you'd like to go. If you come down the westside hwy you just basically follow the signs to the lincoln tunnel and you'll see the lot there - huge like the whole block.
I don't know anything about the bronx zoo stuff, sorry. Have a great trip!