Contrary to the popular opinion The City is not that big. So let's lay out a few rules that will help your search:
- If you are going to stay in Manhattan there are very few places that have more then a 4 block walk to a subway that will take you almost anywhere you want to go, so drop a pin and there you will stay (just don't stay in the parks police doesn't particularly like that :) ).
- Areas of Brooklyn and Queens as well as some places in the Bronx also offer great views and ease of access to the city, such as Williamsburg, Brooklyn Heights have great views of east and south sides of Manhattan as well as access to the Subway so 15-20 minutes will get you to practically every place of interest in Manhattan.
- Consider looking in Hoboken or downtown Jersey City. These can be slightly on the expensive side but have access to PATH which runs 24 hours and buses that get you in and out of Manhattan really quickly (having lived in Jersey City time to commute to Times Square was less then for some Brooklynites).
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.