I'd suggest taking a LIRR train from Jamaica to (say) Patchogue; ride east from there to East Hampton or so; north from there to Sag Harbor, cross Shelter Island, Greenport, then head back west along the north shore for a bit, then down and along the Peconic Bay a while, through Riverhead (not so nice, but there's gotta be a cheap hotel there), then through the pine covered hills west of there, ending up at another LIRR train station, such as Ronkonkoma or Port Jefferson Station. I can give you a pretty good route for most of this. Eastern Long Island is extremely varied, makes for interesting riding, and is pretty flat.