Thanks for including this comment. I find it the ultimate irony that someone posting from a trailer in backwoods Texas has the audacity to call NYC a pit. :) Happy New Year to the NYC freepers!
Here is a link for both:
http://www.amnh.org/museum/welcome/index.html?src=i_plan
http://www.metmuseum.org/
Also, you need to see a ballet at Lincoln Center. Here's a link for the New York City Ballet which resides at the New York State Theater:
http://www.nycballet.com/nycballet/homepage.asp
You can purchase tickets at their website. Also, a better ballet company which also performs at Lincoln Center at the Metropolitan Opera House is American Ballet Theater. Here's their link:
http://www.abt.org/
While traveling around the city, you should really explore the subway system it's fast and not difficult to figure out. It will save you a lot of money during the day and you can just rely on cabs in the evening.
If you have time, you could also save on Broadway tickets by standing on line at the Kiosk which is located on 45th St and Broadway. They offer reduced tickets for the same evening and post the shows outside.
These are just a few highlights. How much time are you planning to spend?