score:6
Contrary to the popular opinion The City is not that big. So let's lay out a few rules that will help your search:
Sights. Considering what you have listed I would assume you wanted to see Grand Central Terminal rather then Penn Station because the original Penn Station is gone.
Hotels. Hotels could get expensive in New York City and around Christmas and New Years you might have to pay arm, leg, and a few other body parts for a room. If you are looking to stay a week you might look at AirBnB to see if you can rent an apartment. One thing though is there are a few Supermarkets around so if you decide to cook locate those first.
But in all enjoy the city.