I can't speak for bars and clubs, so I'll defer that info to those who are more familiar with the NYC bar scene...
Definitely hit the big museums if you are into that - Museum of Natural History, Hayden Planetarium, Met, MoMA.
We have some truly awesome food options. I recommend grabbing cheap sandwiches at random delis mid-day, and saving the indulgence for mid-level restaurants...
For first time tourists, these are my recommendations:
32 Spring St., New York, NY 10012
between Mulberry and Mott Sts.
Zagat's has named this place "Best Pizza on the Planet" - and I'm not prone to disagree.
466 Amsterdam Ave
Convenient if you go to the Museum of Natural History or Hayden Planetarium. The best sushi I have yet experienced in NYC. On my first encounter with their "Caribbean Roll," I made such a fuss that the woman at the next table ordered one herself just to see what the fuss was about -- think "When Harry Met Sally." They also have locations that I haven't tried at 1501 2nd Ave, and 265 E 78th betw 2nd & 3rd Aves.
75 Ninth Avenue
One of my favorite Brunch places. There is sometimes a wait, but the food is incredible. And afterward, you can browse the next-door Chelsea Market, which is well known for specialty food shops and various odds and ends.
167 Mulberry Street
Good Italian food is far harder to find in NYC than most would imagine. (There are italian restaurants everywhere, but I have difficulty enjoying a restaurant if I could easily make better versions of the same food myself). La Mela is a great, nearly overwhelming, place to eat until you are ready to burst. It's not a gourmet place, but rather an awesome example of family style comfort food.
47 Ave B (Near 4th St)
This place can be loud, but it is FUN, and the combination of awesome food -- and belly dancers (yes, one is male) -- makes it one of my favorite restaurants in the city. The chicken bastilla (chicken, basmati rice, raisins, and spices, baked in phyllo and dusted with cinnamon and powdered sugar) is one of my favorite meals of all time.
712 9th Ave.
I can't find a web site for this place - maybe because it is TINY. But the food is cheap, and yet it's one of the best Thai places at which I've eaten.