I have lived just north of the city for over 15 years. Have done the tourist thing many times with friends and relatives.
Downtown
Depending on time I would skip the Statue/Ellis Island tour. It takes the better part of a day, you need reservations, and they don't let you into much of the statue. A quick way to see the statue is to take the Staten Island Ferry which goes right by it. Free. And if you hustle when you get to Staten Island you cam get the return ferry in 5 minutes. If you have the time, by all means do the Statue and Ellis has a great tour.
Just north of the ferry is Battery Park, the stock exchange, Trinity Church, the Fed building steps where Washington was sworn in as president, the bull statue, and the 9-11 memorial. You should look on line and get reservations for the memorial as it can get crowded.
Walk through Chinatown and Little Italy, just off Canal St. Right next to each other.
There is a tenement museum/tour that is interesting. Done it several times.
Walk across the Brooklyn Bridge.
Places to eat
Pepolinos - small Italian place. Just off Canal on west Broadway. Highly recommend. Reasonable price. Best cheesecake in NYC.
Cuba - Cuban Food, outstanding mojitos.
Blue Water Grill - Union Square. Seafood.
Spice Market - Thai/Asian fusion
Mid town
We don't do the Empire State Building anymore. We find the Top of the Rock at Rockefeller Center better due to crowds. But if time isn't an issue always good to say you did the Empire State. At Rock Center is the ice skating rink. If late Nov they may have the tree up and this will be very crowded. See St Pats church across the street. Go see Grand Central especially at rush hour If Christmas time see the light show at Saks
Theaters - always fun. Go to Broadway.com. Pick out what you want to see and pay the price. All the theaters are small so you can sit in the cheap seats just fine. There is also a discount ticket place in Time Square if you aren't particular.
Have a hot dog from a street vendor, or the roasted nuts if cold enough.
Places to Eat
Bar Americain - Bobby Flay's place. Steaks. Good food but a place to be seen so get a reservation. Pricey
Carmines - Tourist trap in Time Square but surprisingly good. Family style Italian.
Uptown
Walk through Central Park, got to the Museum of Art or Natural History. Go to the Dakota where John Lennon was shot.
I find cabs to be a reasonable form of transit in NYC. Try the subways. Confusing and chaotic if you have never done it but something you should experience.
Yelp is very useful for finding places to eat. Check out a site called Trip Advisor for things to do.
There is a hop on/hop off bus service for tourists called the Circle Line. Never done it but it would seem useful.