Just a couple of thoughts...
The Statue of Liberty is always a great location. If you can get over to Liberty State Park here on the Jersey side of the Hudson you will get some tremendous views of the Manhattan skyline, especially the on-going build of the Freedom Tower. Also, you can get some great views of the Verrazano Narrows Bridge.
MSG has just undergone a massive renovation. As such the "All Access Tour" is currently closed. I'd suggest checking out
this site for more information.
For Broadway shows, you may want to check out the
TKTS Discount Booths for less expensive tickets. However, keep in mind the tickets sold are for the performance on the day you buy the ticket(s).
Depending on your interests, you may also want to check out the
Museum of Natural History, and the
Metropolitan Museum of Art. The
Rockefeller Christmas Tree will still be up. You may also want to take a walk through
St. Patrick's Cathedral. Of course there is always the
Empire State Building.
As for Yankee Stadium, if you want to see Monument Park, it is usually open up to a half hour before the start of the game. The vantage point to the field can be quite unique because of how close you are to the end zone. For Yankees fans and those who love history, I would definitely recommend the Yankees Museum which is located inside the Stadium by Gate 6. I do not know if it will be open during the game, but I believe it will be open prior to the game.