Minnewaska State Preserve has ~32 miles of carriageways for mnt biking. Entry is $6 per car. Lots fill up quickly on weekends. Can be crowded, weekdays are best. Be sure to swim in Awosting Lake mid ride!
On the east side of the Hudson I highly recommend Taconic Hereford Multiple Use Area, 18 miles of dirt logging road and singletrack (moderate to technical). For singletrack training this place is GREAT! Bring plenty of water. Parking and entry is free. There is really no map, the major snowmobile trail is blazed with DEC red circles, the single track are informally blazed, sometimes not blazed. Its a fun place to get lost and then found in. Its only about a thousand acres, though, so you really can't be lost for too long! Its mountain bike training heaven in there! To reach it, take the Taconic State Parkway north to Tyrell Rd (~15 miles north of I84), park at the end of Tyrell. Oh, there are also a bunch of dirt roads next to the park.
Sabrina