There are some cycling events during the time you are here that might pique your interest-- The Montauk Century is on May 16 (if that is within your "next few weeks" timeframe) and registration is still open:
http://www.5bbc.org/montauk/
There is also the TD Bank NYC 5-Borough Bike Tour (which has a Century route I believe) on May 2, but unfortunately registration is closed for that.
Or if you'd like to ride on your own, you can always do the Hudson Greenway (west side of Manhattan), across the George Washington Bridge then up U.S. Route 9W to Piermont, which is a popular route among seasoned NYC-area cyclists.
Another 70+ mile round-trip ride is the Westchester South County then the North County trail, which will bring you all the way to Lake Glenida in Putnam County.
http://www.westchestergov.com/parks/trailways.htm
Or you can take a Metro-North Commuter Railroad train from Grand Central Terminal in Manhattan 70 miles north to Wassaic to ride the Harlem Valley Rail Trail (10 miles southern trail section, 8 miles on Route 22, then another 2 miles on the northern trail section to Copake Falls. Round trip 40 miles). Very scenic ride, that one.
http://www.hvrt.org/ (Note: To do this, you need to buy an MNRR bike pass for $5 at Grand Central to bring a bike onto a Metro-North train.)
Lots of good riding to be had in the NYC area!