i'll try to post something remotely helpful:
1) yeah, stay the fuck away from wall street. i'm from new york and i haven't gone to the empire state building or any of that other shit since i was really young. it's whatever. honestly, you won't really be missing much other than standing on a tall building.
2) eat nothing but pizza. but, if you want something other than pizza: take the L to the myrtle-wyckoff stop, go out the entrance on wyckoff and get tacos and stuff from the truck out there. shit is cheap and delicious. make sure you go to the one on WYCKOFF... not the truck around the corner on myrtle.
3) ride elevated train lines. all of them.
4) go to coney island and walk on the boardwalk down to brighton beach. get food there.
5) go to the cloisters: http://en.wikipedia.org/wiki/The_Cloisters
6) go to astoria, and take a photo of yourself in front of the entrance to rykers island. you'll be the envy of all your friends. if nobody has done that planking shit in front of the sign, you should do that.
go to astoria park, too.
7) go to the met (http://en.wikipedia.org/wiki/Metropolitan_Museum_of_Art) and do NOT pay the suggested 20 dollar donation. give them a quarter.
beyond that, i don't know what else to tell you. don't buy weed in washington square park. and if you really want to go to the top of something tall AND times square, theres a hotel in times square with an open roof door and it's cool to hang out up there looking at all the idiots trying to get into the aforementioned times square tgifridays.
hope this helps.