Fuzzy made some really great suggestions about driving.
Katie, if you can break up your trip over a few days that sounds like a great idea. The airfare sounds really expensive.
I'll look into some car storage places for you (my twin brother that lives in NYC is in town for the weekend and might have some good leads).
PS: you might want to look into a monthly pass at a local garage, as it is much cheaper (~$300).
Central Parking Monthly Rates