jkuper,
Westerville, which is a little south of Sunbury on Rte 3, has a well developed trail system. I rode my bike on them all the time when I lived down there. I think the Genoa trail is finished and goes all the way to Galena. You can pick up the trail system there although it in not technically part of Westerville's system. McNamara Park has bathrooms and water. The fire station at Rte. 3 and Big Walnut Road will also refill your water bottles for you.
Check out the link:
http://www.westerville.org/index.aspx?page=495