Hugglez, since you're traveling to New York City in the Winter make sure you pack plenty of warm clothes. Sweater, scarf, a coat, a pair of glove and a knit cap.
In regard to thing to do in New Yorker City, may I recommend the following.
Landmarks
-Empire State Building
-Statue of Liberty/Ellis Island
-Rockefeller Center and the Top of the Rock Observation Deck, as well as the Christmas Tree (and a tour of NBC studios)
-Times Square (no trip is complete without a visit to the"Crossroads of the World")
-Lower Manhattan/Wall Street Area
-United Nations
-Central Park
-Brooklyn Bridge (you can walk across it too)
-Grand Central Terminal (largest railroad terminal in the country)
-A Ride on the Staten Island Ferry (its free and you can see the Statue of Liberty as the ferry crosses the harbor)
-Sightseeing tour on a Double Decker Bus
Museums
-Museum Mile (Fifth Avenue from East 82nd to East 103rd Streets)
-Museum of Natural History and the Rose Center for Earth and Space (formerly the Hayden Platerium)
-MoMa
-Whitney Museum of American Art
-New Museum of Contemporary Art
-Madame Tussaud Wax Museum
-New York City Fire Museum
-New York City Police Museum
-Transit Museum
-The Intrepid Sea, Air and Space Museum
-Manhattan Children's Museum
-Sony Wonder Technology Lab
-New York Hall of Science
-The Bronx Museum of the Arts
-Brooklyn Museum
-Milk Gallery
-American Craft Museum
-Museum of American Folk Art
-Museum of the Moving Image
-The Paley Center For Media (formerly the Museum of Television and Radio)
-The Municipal Art Society
-Jacques Marchais Tibetan Museum (only Tibetan museum in the USA)
-Alice Austen House (one of the first professional women photographers, many of her prints are on display, and her home had an absolutely unbelievable view of the harbor)
-Snug Harbor (nation's first and only home for retired mariner, its now a museum complex)
Other Attractions
-Broadway Show
-Christmas Spectacular at Radio City Music Hall
Shopping
-Macy's (West 34th Street and Broadway in the heart of Hearld Square)
-Bloomingdale's (Lexington Avenue at East 59 and East 60 Streets)
-The shops along Fifth Avenue (just don't max out you credit cards)
-FAO Schwarz
-Toys "R" Us in Times Square
-Lord and Taylor (5th Avenue at East 38th Street)
-Chinatown/Canal Street Area (if you want to go on the cheap for the stuff you can't get on Fifth Avenue)
-NBA Store (for the basketball fan - 5th Avenue at East 52nd Street)
-The Apple Computer Store (East 59th Street and Fifth Avenue)
-The Time Warner Center (West 59th Street - Columbus Circle)
-Hershey Store (for those with a sweet tooth)
-M&M World (49th Street and 7th Avenue)
-Grand Central Terminal (for the shopping)
-H&M
-Century 21 Department Store (Church and Cortlandt Street)
-forever 21
-Barneys New York (660 Madison Ave)
-Abercrombie & Fitch (5th Avenue @ 57th Street and Water Street between Fulton and John Streets)
-American Eagle Outfiters (4 locations in Manhattan)
-Urban Outfitter (8 locations in Manhattan)
-Manhattan Mall
-Queens Center Mall
-Queens Place Mall
-Roosevelt Field Mall (on Long Island)
-Fulton Street Mall
-Kings Plaza Mall
-Woodbury Common Premium Outlets
-Garden State Plaza
-The Westchester Mall
-Palisades Center Mall
-Westfield Sunrise Mall
-Green Acres Mall
-Jersey Gardens
Restaurants
In regards to place to eat in New York City. There are thousands of the restaurants in the Five Boroughs of New York City. Depending on your taste, your budget and your preferred location, may I recommend the links below.
http://www.urbanspoon.com/c/3/New-York-restaurants.html -- Urbanspoon. You can find restaurants either by price, location or cuisine.
http://www.ny.com/dining/ -- NY.com. You can find plenty of restaurant information at this link. Everything from H&H Bagel to fine dining at Le Cirque. Bon appetit!
I hope this information is very helpful. If you have any questions or need travel directions while in town, just drop me a line by clicking on the avatar and e-mail icon in the profile. I'll be glad to help.
Good luck
Native New Yorker