Lincoln Square is where almost all of the big players in cultured entertainment perform so it's pretty easy to find stuff to do.
1. Alvin Ailey Dance
2. The Philharmonic
3. Central Park
4. The Met Opera
5. Try to catch Bob Cunningham snapping pics for the Times outside his Carnegie Hall home
6. Manhattan Theatre Club
7. Dinner at Jean-Georges (or just drinks because it's crazy expensive)
8. Columbus Circle people watching
9. The Ballet
10. The architecture in the Upper West Side is breath taking. I walk around and just gawk at the bajillion dollar homes in this area.