Also, if you want to stay off the streets in Manhattan as much as possible it's very easy to get on the East River Greenway from the Williamsburg Bridge:

http://ridewithgps.com/routes/126285

Switch to the satellite view to get the idea, there is an overpass over FDR right by the bridge.

To get back on the Bridge from the greenway do this:

http://ridewithgps.com/routes/126289

Same overpass just take the road on the other side of the bridge. Please do not ride against the traffic!