Thanks a lot veen. I'll definitely put the Rockefeller Centre (and therefore MOMA) on top of my list. Speaking of museums, word has it that the Tenement Museum is a total gem, so I'll probably give that a look in. And yes, I also plan to spend at least several days involved in aimless wandering to see what comes up. Restaurants are going to be slightly complicated because my girlfriend is vegan. Hopefully TripAdvisor will help there (I'm downloading the app now). The city is supposed to be a vegan mecca, anyway. Thanks again.
One of the good things about NYC is that the restaurant market is so competitive that shitty restaurants have a difficult time surviving. They have to be a bit expensive, because real estate is so valuable, so no one is going to pay premium prices for shitty food. Therefore, you can find something decent (including vegan food--especially in trendy Brooklyn neighborhoods like Williamsburgh, Greenpoint, Bushwick) pretty much where ever you are. If you can't find good food in NY, you really have to be trying not to.