We always take a cab from the airport because renting a car and having to pay parking is very expensive.  I mostly have when we travel for shopping several people with us to split taxi fare....if we are shopping where we can take the subway we do that.  I however never take the subway at night so we always take a taxi.
I LOVE the Tic Tock Diner for breakfast and sometimes if we don't have time to go out for lunch or dinner ect...the diner is good and so is the bar restrurant 

The hotel can get you broadway tickets too but we always buy them at ticket master online a month or so before we go to NY.  We've already made dinner reservations to a restruant one night already.  I always have hotel booked, airline tickets and restruant reservations and broadway tickets way in advance LOL...
Professional wear if you are showing and casual wear if you are just watching.  Bring layers and I suggest a down coat it keeps ya warmer and of course I always have my UGG boots!  Looks like this trip to NY might be on the colder side the way it's going now! 
Hope this helps,
Donna