We booked a hotel (The New Yorker) through a travel agent so we knew exactly what taxes etc we were paying and it included a transfer from the airport. The hotel had a 24hr diner, reasonable bar and had just been re-decorated. If you like Art Deco and the 20's feel then NY is for you. The hotel was about 1 block from MSG, 15 minutes walk from the Empire State and we had to go past Macey's to get there.
This year check out the weather in NY as it can get colder than a cold thing in a fridge and work out what is feasible. Crap weather - ride the subway! It's dead easy.
My tips (not all for the same day!!!):
Go early to Empire State (weather dependant) to avoid the "lines" (queues) then you can get some fresh air at the top without it being too crowded. The extra cost to ride another couple of floors up from the observation deck isn't really worth it.
Walk up 5th (?) from ESB toward Central Park and watch how the shops change from tourist tat to $$$$$$. Seriously there are some shops near central park that may as well have a big sign outside saying "No poor scum". Even the window dressing was exotic.
Visit Trump Tower. Saks etc, Go for a walk in central park. Go to NY MOMA (Museum of Modern Art) if you like that sort of thing - I think it was mindblowing but I love all that stuff. Rockefeller Centre - see later in this post.
Eat somewhere down a side street where the locals go. Talk to people, go to a sports bar and ask someone to explain whatever is on the TV (even if you already know) great icebreaker.
Go to Grand Central Stn and look at the ceiling and take in the atmosphere before going down to the food hall area and eat whilst commuters rush past. High end dining to burgers, side by side. I had pastrami on rye (always wanted to order that!!) and it was ace.
Visit Chinatown at the weekend and watch chinese people singing and playing instruments and then cross the street into Little Italy. Have a coffee and an ice cream (even in December). You have to realise that they do really talk like that and you aren't on a Soprano's film set.
Weather and visibility dependant - find out when sunset is and 45 minutes before hand walk across the Brooklyn Bridge from Manhattan. Turn round and then slowly walk back and watch all the skyscrapers light up - very atmospheric (but not in the pissing rain!)
You could book tickets to go up the Statue of Liberty and peer out her crown. We didn't but heard that queues were long (in November) unless you already had tickets - it is also very cramped.
If going to S of Liberty also go to Ellis Island. If you are in any way interested in migrant history or the history of the USA this will take several hours to get the best from it. It was done-up about 8 years ago so it should still be OK.
If the visibility is good do "The Top of the Rock" at the Rockefeller Centre at night, and realise that after the lift there are about 2 floors more to walk up. The advantage is that you see the ESB all lit up, and the Chrysler building and a corner of Times Sq (plus obviously the rest of NY).
Then go to 42nd street having already booked your shows on the internet.
Been once - for 5 days - and really want to go back. You will have fun.
PS: Manhattan is safer than a safe thing (one of the safest cities in the world) but if it doesn't feel right, turn round and walk away.