I've only been "roadbiking" since last October, but I've found plenty of good rides in and around NYC. I was pretty nervous to ride in the traffic at first, but you get used to it pretty fast and I don't hesitate to go anywhere now. You just have to use your head, don't be a hot dog and pay attention to what's around you - watch out for idiots opening car doors without looking.
From where you are, you could just shoot crosstown on 14th and take the westside path to 60th (that's where it becomes Riverside Park - you'll see the sign). Go east on 60th two blocks, cut back to 58th, and take that to the park. No cars or traffic lights on the path and you can do 15-20+ mph most of the way.
I'm in Central Park most weekday evenings after work, that's about the closest place to get a workout and it's not too crowded. During the cooler months the weekends are okay too. Beware of people going around the loop wrong way, especially at or after dusk. There have been some very serious accidents (i.e., R.I.P.) caused by people doing that; always use lights.
That westside path goes all the way from South Street Sea Port/Battery Park to the end of the island, it's a nice ride. There's a detour onto the street at 125th, but it resumes after a couple of blocks - follow the signs. It ends at some stairs at 218th Street, just carry the bike down and follow the on-street bike lanes. You can go into the Bronx, and on to Yonkers (about a 50 mile round trip) or beyond; or cut across the top of the island and come back down the eastside path to South Street Seaport again. Just follow the bike signs.
You can get the GW bridge from that westside path around 180th Street. Go over into New Jersey and take 9W to Nyack (65 mile round trip) or beyond.
You can take the Staten Island Ferry from Battery Park (it's free and runs every half hour) and go around Staten Island.
You can go Prospect Park, via the Brooklyn Bridge, and pick up the bike mall along Ocean Parkway. That will take you straight to Coney Island. At Coney Island, get on Neptune and follow that to Sheepshead Bay (become Eamons Avenue). When you get to the Belt Parkway, you'll see a bike path and you can take that to the Marine Bridge or (to the end) the Cross Bay Bridge. Take one of those to the Rockaways, go to the far side, and ride for miles along the boardwalk into Far Rockaway (if you return now, it's a 60 mile round trip via the Marine Bridge or a 65 mile round trip via the Cross Bay). At the end of the boardwalk in Far Rockaway, you can go across the bridge to Atlantic Beach and go through Long Beach and Lido Beach to the end of the peninsula at Point Lookout (80+ mile round trip).
If you're really ambitious, at the end of the Far Rockaway boardwalk, pick up Beach 9th Street and take that to Empire. Empire runs into Broadway, which ends at Merrick Road. Go right and take Merrick Road to the Wantaugh State Parkway (around Belmore). Go under the bridge, make the second right and enter the park you'll find at the end of the street. On the right hand side, there's an entrance to a bike path that goes alongside the parkway to Jones Beach (that's a round trip of a bit over 100 miles).
Stop in any bike shop and get a copy of the NYC Cycling Map. It's very good and covers all five boroughs. You can download a copy of the Nassau/Suffolk County Cycling Map on the web. Stop in a Staples store and get a copy of the Hagstrom "75-Mile Radius Map from Columbus Circle, NYC" - that'll give you some ideas. It really is a great place for cycling, I've got numerous rides planned - let's just hope we have a mild winter this year...
