You can check out Kissena in queens or ride out to Coney Island. if you have an iphone there is a free app called spokes NYC that is better than the google maps cycling thing.

Also, for a day trip you can take NJ transit/Septa to Philly for like $15. Philly isn't the best place in the world to ride but its a pretty cool city to check out if you're here for a while.