The following are some of the trails I have come across:
River-to-Ridge Trail (New Paltz to Mohonk) Ashokan Rail Trail New York Empire State Trail Minnewaska State Park Preserve
Please take note of the cycling requirements (15mph, carriage roads only, etc.). Mohonk Preserve
The Mohonk trails require a day or annual pass. If you get a yearly pass, you will need the Annual Membership PLUS+ Pass to ride your bike. Poughkeepsie Urban Trail
The Poughkeepsie Urban Trail map is under the About section of the website. I expect this to change as they keep updating the website. O&W Trail (Kingston to Ellenville) O&W Trail (Sullivan County)