The whole island is very nice, although it can at times feel very exclusive or downright snotty. Don't do anything you wouldn't do on Centre Island. I haven't ridden there, but I saw many families bicycling along the streets, seems to be very bike friendly.

Ram Island is very nice. Mashomack Preserve is supposed to be nice, although I haven't been there. The book Short Bike Rides on Long Island contains a route through SI--feel free to shoot me an email and I can send you a pdf of the route.

"Here's a nice route from Yaphank to Greenport. Yaphank is the stop west of Riverhead on the LIRR Greenport line.

Yaphank LIRR to Greenport (40 mi)
north loop around out of train station
L Yaphank Rd
R Main St => Moriches Middle Island Rd
L North => Manorville (at Sleepy Hollow Rd sign on R; follow bike signs)
L Weeks Ave=>North=>River Rd to end (incl BR at bike sign)
R Route 24
L at rotary (94A), go 3/4 way around and turn R into Riverhead
R Main St (Star Confectionery on left)
R Hubbard=>Peconic Bay Blvd to end
L Bay Ave
R Route 25
R New Suffolk Ave
L Grathwohl
L New Suffold Rd to end
R Route 25 to Greenport
follow signs to ferry

This route stays toward the southern side of the north fork. There's also nice biking along the northern side. I did that once from Port Jeff to Greenport but don't have the route. You can figure it out easily enough if you get the LI biking map from LI DOT.

Another option would be to go out along the south fork and take the ferry from Sag Harbor.

Either way, if you're set on biking all the way from Manhattan, just note that you'll have about 40 garbage miles before it gets nice.

Last fall I spent the better part of a day biking and hiking on Shelter Island. If you go around the edges and off to the adjoining islands, you can log about 30+ miles without backtracking. The hike was in the nature preserve in the southeastern portion of the island and was really lovely--woods, fields, and coast. Definitely be sure to get off the main drag on the island, which is to say the main route between the ferries. That road can have a lot of traffic (relatively) but others are very quiet and prettier.

Have fun!
Hannah"

Despite what you may hear, the L.I.E. serivce road is a good way to get out east. I ride it regularly to near Yaphank and pick up the route Hannah mentions to get to Riverhead.
Assume you live in Manhattan, so you can get yourself to the bike lanes on Jewel Ave., eventually 73rd Ave., so we pick up form there.
. . . going east on 73rd Ave.
R Springfield Blvd.
L Union Tpke
L Commonwealth Blvd.
BL Marathon Pkwy
R L.I.E. Service Rd.
L. Woodbury Rd. (Service Road ends just past South Oyster Bay Rd.)
R Sunnyside Blvd (follow signs to 495/L.I.E.)
L L.I.E. Service Road (7-ll on corner on far right)
X Commack Road
BL (follow signs to Service Road)
Caution: traffic to/from Sagtikos Pkwy along here.
BR follow signs to Wicks Rd, caution on merge to right.
continue straight on L.I.E. Service Road.
Service Road will end at exit 66 / Yaphank Rd. / Route 101
L. Yaphank Rd / Route 101
R. Long Island Ave.
L. Yaphank AVE / Route 21.
Follow Hannah's instructions from there.

If you are familiar with the Strwberry Festival Century route or the Montauk Century Route, either one can be adapted to get you to Shelter Island.

Exclusive? Snooty? When I visited Shelter Island many moons ago, I stayed at the Chequit Inn. There was a sailing regatta going on. As we walked up the path to the door, a pair of drunk sailors came tumbling out the door, engaged in a brawl. We stepped over them and checked in.

Have fun.