Best place on Earth.
As for what to do and where to stay it totally depends on what you want to spend. I always stay at Hotel41 (
www.hotel41.com), right in Times Square, middle of everything.
Bring your walking shoes, you'll probably walk at least 5 k a day, I usually average about 8k per/d.
Central park is more amazing each time I see it,
shopping down 6th St and up 5St is cool if you like to shop,
You should probably do the bus tour, I forget their names, but the blue bus company is new, and not as good, the red one is a little more expensive but worth it ... take the tour to Brooklyn if you can. one of the scariest things I can ever remember is being on the top right side edge of a doubledecker going along the brooklyn bridge in the right lane (BTW, don't just look at the bridges, go on one to appreciate how big they are)
Go to the WTC site, they have a good memorial
Learn that the subway is your friend, you'll use it alot
Fulton Square and Piers are cool, just to the east of battary park
Union square is cool at night ... lots of NYU students there
Go to the ESPN zone, and into the TV room, find a recliner, and veg
Go to a football game at meadowlands (via bus from Grand Central Station)
Baseball games and Yankee stadium are cool
Eat at as many places you can ... all food is amazing, even diners that don't look like much have great food.