As always, it depends on what sort of stuff you're into, but here are a few obvious suggestions...
- Visit the Metropolitan Art Museum.
- Walk in central park.
- Drink coffee in Greenwich village.
- Buy t-shirts in the East Village.
- Take a boat out to Ellis island.
- Chinatown.
- See a show of whatever type you're into (Broadway, off Broadway, blues, jazz, whatever. So much choice).
- Take the tramway to Roosevelt island, and take pictures of the Manhattan skyline from the island.
- Walk around the city as much as you can.
- Savour the many excellent diners - great for lunch but especially breakfast.
- Stay away from the Irish bars and you'll be OK