All three sports are huge in the Syracuse area.
For Jet Skis: Oneida Lake is very popular. It's located just northeast of Syracuse....near Cicero. It is also the largest inland lake in New York State, so plenty of room to Jet Skis.
For ATVs, or riding Snowmobiles: Oswego County (the county just north of Syracuse) is probably the epicenter of these two sports in Upstate NY. With plenty of lake effect snow in Oswego County, people from all over the northeast flock there to snowmobile.
Oswego County Snowmobile Association:
Oswego County Snowmobile Association Home Page
Oswego County ATV Club:
Oswego County ATV Club Home