There's no way you'll see everything NYC has to offer in a week, so to make the most out of your trip I suggest
bringing some speed or redbulls planning out **** accordingly.
Actually thats not true at all, getting around is easy enough that you could very well do all the major sight seeing in a day if you wanted to. I feel the biggest time waster is the Statue of Liberty and Empire State building. Long lines and such. It really depends on what you want to get out of your trip though. Something like the Statue of Liberty.. You could either see it from a view finder from Liberty State park or take the (most likely expensive) Liberty Line trip to the island itself. While there, you can choose to gawk at it from below or climb to the top. I've lived just outside NYC myself and I've yet to ever go inside the damn thing. Lines too long, way too hot (in the summer of course), it's just not for me. Oh and they've never had the torch open when I've gone, which if I really wanted to climb that high for possibly the best view of NYC, it'd be from there not the crown. So yeah, if you're like me maybe you won't even want to go to the damn isle.
Empire state is just as intense from the outside looking up as it is from the inside going down, but instead of pretty plaques on the wall, an ear popping elevator, and a potential virtual cab ride (at an extra charge) somewhere on like the 90th floor, you'll get to be outside taking in one of the best things Manhattan has to offer; loads of beautiful women. I can guarantee you'll be looking at women more than the Empire State building if you're outside of it, especially if you're on E. 34th street which is basically the fashion district. The most attractive women going in and out of Victorias Secret, H&M, Macys etc, all on one lil corner..
As for Central Park, keep in mind it's fucking massive so you might want to plot a course and pick something in it you want to see specifically, otherwise you'll end up doing a lot of walking in the most boring spots. For me it's fine to waste hours wandering around aimlessly because I can always go back, but if its your first time, I'd hate for you to see only the dog park and peanut vendors. I feel that the south end has more to see (zoo, skate rink, carousel, the famous tavern on the green) then again I've yet to go to the norther part of the park.
I don't know if it's the same as "Ray's Famous" pizza chains in NYC, but I can tell you Ray's (Pizza Bagle Cafe) in the village is fucking awesome before and after a night of drinking. Speaking of food, if you're interested in theme restaurants, I've heard Jekyll and Hydes is fun but I've never been to it myself so i can't vouch for it. I will tell you that Mars 2112 on broadway SUCKED when my gf and I went, then again it was most likely on an early Monday evening or something where any place would be really lame. Keep in mind these places are pricier than most and, again speaking from experience with Mars 2112, wasn't that good.
NINTENDO WORLD STORE. And get me stuff. 
The most obvious answer actually, since this is a nintendo site you're on after all. I haven't been there recently, I know it's been renovated so I'm curious to see what it's like now myself. Its always a really cool place, they have tons of game stations to play on, I'm sure they'll keep the mini nintendo museum that shows off things like ROB, the original famicom, cool **** I never heard of before seeing it there myself like the NES Keyboard, they even have some of those hanafuda (sp?) cards! My favorite piece was always the gulf-war gameboy. Don't ask, just go see it yourself. They have a lot of cool merch too so try not to spend all of your money there. Literally right outside the NWS is Rockefeller Plaza which is a nice touristy site, and if you're lucky maybe Nintendo or NBC will be holding some event outside that you can look upon.
Oh and it don't forget to check out Toys R Us in Times Square, they have some cool displays on the top floor!