Yeah, I live in the Finger Lakes area of NY. I go to the ADK's for hiking. Other than a few spur trails, there are not too many in western and central NY. The Finger Lakes Trail or North Country Trail (same trail from central to western NY) is fairly well populated with some good views of the various lakes, mostly wine country or dairy farms.
I can recomend the older Black River Trail but I think that was converted to a snowmobile/ski trail several years ago (10-20.) They just proposed a final route for the NFCT through the ADK's, but you are at least 3 years too soon. They still need to finalize the pollo-tics and build a good section of it.
There are several in the central area, Ha-de-ran-da is a hiking area just east of Old Forge. This is roughly an hour from Utica (on the thruway/Rt 90 to 12north to 28north.)
Good hiking in this area...several possible loops or good for an out'n'back. There is also several day hikes around Old Forge. Further north, 45min or so, is the town of Inlet. It has several trails (Bear Mountain, Snake Pond, Bug Lake, Eagle's Nest, etc.) Also the Moose River Plains, but you really need a high clearence vehical for that. There is a moose (Harold the moose) that hangs at one of the ponds up there, Helldiver Pond I think.
You really want a canoe to do more.