If you say that you're lacking experience, I have a recommendation. Get you and your bike on the 6 train. Ride it north right to the very end, at the Pelham Bay Park stop.
From there, hop out and ride northward on Shore Road. You'll cross a bridge and when you come to an intersection with traffic lights, turn right. You'll know you're at the right place when you see a horse stable to your left. Follow the signs to Orchard Beach.
When you get to Orchard Beach, follow the dirt path and it'll lead you to the entrance of a nature trail. This nature trail is set on a hill - it covers the circumference of the peninsula, but also has tons of smaller trails leading to the middle of the peninsula which is the summit of this small hill. If you zigzag the trails, ride one way, then ride it backwards, you can squeeze about 5 miles of pretty easy riding there. The hill climbs are short and work well for training purposes without actually killing yourself.
Download this map that covers all the bike routes in the boroughs of NYC:
http://www.nyc.gov/html/dot/pdf/2004bikemapfront.pdf
In the meantime, I've drawn you a map to take you from the subway stop to Orchard beach. Follow the purple route and you can't go wrong. When you're done, ride out to City Island for a few well-deserved beers, catch some sea breeze, then ride home.
Enjoy!
