Car,
One of my very favorite days in New York City goes like this: spend your morning at the Metropolitan Museum of Art, eat lunch in Central Park at the--I think its called--the Park View Cafe (I'll check on that for you), and then walk across to the other side of the Park to the Museum of Natural History. Both museums are absolutely incredible. You will be completely exhausted by the end of the day, but its so worth it.
If you love to shop, then no trip to New York is complete without a stroll down Fifth Avenue. Its a shopper's mecca!
If you walk on 5th down to the 50s, you can hop over to see St. Patrick's Cathedral and Rockefeller Center, which are also must-see landmarks.
Don't forget downtown, either. Chinatown and Little Italy are fun places to spend an afternoon. Its also fairly easy walking distance to City Hall, the government buildings, TriBeCa and Ground Zero if you want to pay your respects.
Or, if you head in the opposite direction from Chinatown you could hit Soho and Greenwich Village.
There are about a million things you can do! Have fun!!!