Advice for a trip to NYC and DC?

I’m planning a trip with two buddies to go to New York City and DC for around a week, give or take, towards the end of August. We’re driving from Ohio to DC to stay with my uncle for a few days, and then want to go to NYC from there, so I’ve got some questions:

1. Is there a cheap way to drive to NYC, park somewhere, and then ride a train to the subway? We were thinking about taking the DC to NYC bus which would be 27.50 per person per trip, for a grand total of $165. We’re planning on getting daily unlimited Metro cards ($8.50 per day)... So would parking somewhere near NYC and training in be cheaper?

2. In NYC we are planning on staying in a hostel. I’ve heard that the HI New York Hostel is a good one to stay in, but what about the Chelsea Hostel? Any experience staying in NYC on the cheap? One of my buddies is also really into couch surfing, but for 3 18 year old guys I figure hosteling will be less complicated… Unless one of my fellow awesome flutherites would like to host us for a few days (we’d sleep on couches/floors and would pay).

3. We like food, but we’re willing to eat on the cheap to save money. Any guesses as to how much it would be to eat per day in each city?

4. Most importantly, we’re looking for fun things to do – shows (indie rock, diy punk, bars), museums (love met and moma, what else is worth seeing?), and anything else fun/cheap. Our combined interests include art, music, film, photography, biking, and so on. What should we do?

Or if there is anything else I haven’t thought of that you’d have advice on… Let me know!

Thanks!