Bring the mountain bike. Lots of great riding in the area. (If you aren't from Florida, the riding will likely be better than what you might think a relatively flat state like Florida could offer. Think old mining quarries.) Boyette, Alafia and Carter Road provide challenging and fun riding. Flatwoods/Trout Creek/Morris Bridge is a good trail system for an easy, fast, flat trail ride. Swampers are famously accommodating, so post a message before your arrive. Someone will likely offer to show you around. You can also join the Sunday club ride. Check the calendar on this site. You don't have to be a member.
October is generally pretty good, too.