Read http://www.forgotten-ny.com/ before setting any agendas and if you have some time to spare, there is some awesome history to find. I lived there for nearly 20 years and it's endless the amazing things you can find just a short distance from anywhere.
One of my stops is *always* the Dakotah and Strawbberry Fields followed by a walk through Central Park. Up on the Northwest side is the lake/castle that's a must see too.
Right at 72nd and Columbus (close to the Dakotah) is the greatest pizzeria in NY.
C. Genrich