There is the Santa Rosa Lake State Park, with trails for hiking or biking. It's just north of town on state rte 91. That's it that I know of. We did not go to the park on our trips through here.
I don’t know of any. It’s basically in town, if you could call it that. It’s very close to the interstate. We took a drive around the area but it’s all pretty remote. You could probably bike on the secondary roads as there was virtually no traffic.