Just came across this thread and hope this information is not too late.
I love NYC and have tried to go at least once a year since 2004.
There is an organization there called Big Apple Greeter (
Welcome to Big Apple Greeter). Basically this organization matches locals with visitors free of charge. The local will spend about 2-4 hours with you showing you their nieghborhood or a part of the city that they are extremely familiar with. Also during the visit, they will show you how to use public transportation. While you can select the specific areas you might like to visit, your best bet is to mark "greeter's choice." This opens up more opportunities. Applying does not guarantee a greeter, but it is worth trying. You are not paired with any others, so it is just your greeter and your specific group. I tried on three previous trips and never got a greeter until this past July. Our greeter took us on a terrific walking tour of Central Park that was fabulous. We ended up spending about 5 hours with him and covered the entire park.
Goldstar requires that you register, but there are some pretty good savings on tours (
http://www.goldstar.com).
For theater tickets, try Broadway Box (
BroadwayBox.com: free Broadway shows Discount codes for broadway theater tickets). They have pretty good tickets for non-sold out shows and you can order the same day and pick your tickets up at will call. In addition to the TKTS booth that is in Times Square, there is also a booth down by the South Street Seaport that is usually less crowded if you happen to be in the area.
Also, for sold out shows (Jersey Boys is awesome) you can sometimes find tickets available through Ticketmaster.
The Staten Island ferry is free and provides a really nice viewing opportunity for lower Manhattan. That includes the Statue of Liberty, downtown skyline, Brooklyn Bridge, etc. No stops, just to Staten Island and back, but it is a nice ride.
For something a little bit different you might want to check out Accomplice (
Accomplice | New York City & Hollywood | Game, Tour, Show & Scavenger Hunt in NYC, NY & Los Angeles , CA). There is a tour for downtown/Tribeca/Chinatown and one for Greenwich Village. I haven't done the Village one yet, but the downtown one was a blast. Very fun and funny.
If you like to research, check out the New York City forum on TripAdvisor.com. It is a wealth of information.
And last but not least, have a great time!