What month of the year?
If it is during baseball season take the Staten Island Ferry and see a Staten Island Yankees game.
Like Vronsky said, Naturla History is amazing for everyone, but for an 11 yr old boy, it is magical. Same wiht the Met, the paintings will bore him, but he will likely love the hall of weapons and all of the armor, and the section of egyptian stuff is awesome and includes an entire temple reassembled indoors.
Central Park Zoo can be done in an hour or two, then chill in the park. Walk to the castle, or do some free fishing in the harlem meer if it isn't dead of winter. If you are here in the winter go skating at the rink.