Is there anywhere to check luggage while you visit the museum?

Coats and small bags may be checked inside the Theodore Roosevelt Rotunda, inside the main entrance on Central Park West. There's another bag check at the Rose Center for Earth and Space, open from September - March only. Luggage, small carry-ons, and oversized backpacks cannot be checked in the museum.

By the air and space section entrance there is a coat check in and you can also check in bags. I don't know about any luggage though.

I don't think so!

As I recall there is no place to leave your luggage. But usually the NY hotels can keep them before/after the check-in/check-out.