There are loads of cycle paths in Queens. You can ride all round the top of the borough by the water and La Guardia airport and there are several parks with cycle paths through them and the Brooklyn-Queens Greenway links the two boroughs via a number of parks. You can ride over the Queensborough Bridge cycle path and this lands you in Manhattan, about 4 blocks away from Central Park.

I lived in Astoria for many years. After much exploring I came to the conclusion that when you live in Astoria, the best local cycling destination is Central Park. To get there via the Queensborough Bridge takes about 20 minutes.

Once you get here, you can get a free cycling map of New York City either from most bike shops or directly from the NYC Dept. of City Planning, Transportation Division (212-442-4711). It indicates all bike paths, on-street bike lanes and recommended streets for cycling in all five boroughs. It also indicates locations of bike shops.

You can also take your bike on the subway, so if you don't want to ride across the 59th St. Bridge to get to Central Park, you can take the N train from Astoria. That makes it easy to join any New York Cycle Club ride that leaves from the Boathouse in Central Park. Then you'll learn all kinds of places to cycle.

http://www.transalt.org/calendar/century/map.html

That's the site of the TA map for its century. It runs the course along the water in north Queens. Maybe there's a cue sheet somewhere.

The NYC map has the paths too. And with greater detail.

Also, explore Roosevelt Island.