I lived in fort Washington for a bunch of years - Fort Tryon Park is the city's best kept secret and that museum is really neat - especially in the spring with the lavendar garden...
Just take the A train north...
and if you're feeing adventurous
you can walk across the George Washingon bridge to new jersey -then just turn around and come back
see if you can find the
little red lighthouse under the big gray bridge It's a children's story
and I seem to recall there being a new harbor in upper manhattan as well..