NY Yankees/Mets:
Hotels: Stay in Manhattan, anywhere else is a bit of a risk, use Priceline or similar website (FYI, they are expensive). Taxi's to the game.. you can't afford it.
Game Parking:
LOL, if you haven't driven in the City before, don't even attempt it. Parking prices, LMAO, even funnier. For the Yankees take the subway, the B/D from Rock Center, but be careful. To the Mets, take the 7 from Grand Central & pray you can catch the express.
Tickets:
For the Mets you shouldn't have a problem, but for good seats you may have to scalp. The Yankees may be a different story. But trying on the website is a good place to start. As for good seats, you probably don't have enough money.
What to eat at Ballpark:
You're in NYC, eat the Pizza or the Dogs. While you wont' be able to afford the beers at $8, they sure look tasty. Of course they have the rest of the average tasting ballpark food as well.
What to do/eat in the City:
It's New York, you can do anything you want. Most of the food is good too. The list of good places to eat would be endless.
Disclaimer: (This was compiled slightly in gest, while somewhat factual, it might not be completely accurate, but comes from my few of years of NYC experience. For a more complete list a more "seasoned" New Yorker would be more helpful, then again, probably not, they'll tell you to 'eff off. )