Long Island Bicycle Club leaves from Westbury High School weekends at 8:30AM, possibly later when cold weather sets in.
Massapequa Park Bicycle Club leaves from Massapequa LIRR train station, Sat's at 8:30 for the C - B and A rides. The AA and Opens leave from Bethpage Library lot (Powell Ave) at 8:30. Then all groups leave from Bethpage on Sunday 8:30. They also have Tues and Thurs AM rides from Boreas Field in Plainview. They have a ride calendar on their site.
The websites list the details.
Then there's Huntignton Bike Club, Suffolk Bike Riders Association, both mostly road and CLIMB, the Mt. Bike club
http://www.bicyclelongisland.org/