Thoughts about NYC: Obviously you're not going to see anything close to the whole city in 12 hours but it's enough to hit a bunch of the high points.
Grand Central is gorgeous and definitely worth a look. MSG is kind of an eyesore from the outside and probably not worthwhile unless you're going to an event there or doing a behind-the-scenes type of a tour.
As others noted, Top of the Rock might be a good spot to hit; you get the view of all the great buildings, including the Empire State Building, without the crazy lines to go up the ESB.
If you're not able to go to the museum (either because it's not open or because you haven't pre-booked tickets), the WTC is probably not worth visiting. Honestly, it's basically just a huge construction site at this point, though my view is presumably skewed by the fact that I've worked a block away for years now, so the emotional impact is sort of blunted at this point. South Street Seaport is also kinda terrible (and really not entirely recovered from Sandy yet either) and I'd say skip it.
Times Square is pretty cool to see but you'll be happy just walking through. Most of the stores you probably have at whatever mall is closest to you at home, they're just bigger in Times Square.
Central Park and the Museum of Natural History (or the Met if you prefer art to science) are definitely a good draw, especially given the awesome weather we're expecting in the Northeast this weekend.
So, I'd say you could make a nice day out of Grand Central, Rockefeller Center, Times Square, Central Park, and one of the museums. You could probably also fit in downtown sights but trying to cram in too much makes sightseeing a chore rather than a pleasure, if you ask me. Those are all pretty walkable to one another, which might be a good thing if, as I mentioned, the weather turns out to be really nice.
If you're looking for places to eat while you're here, let me know if there's any particular meals/types of food you're looking for and I'll see if I can come up with something good.
(Huh. Never expected a thread about the FF in Philly to turn out to be about sightseeing in NYC.)