Don't know your interests but here are a few that have historic, natural and cultural interest.
East Coast:
- Old Deland and Stetson University
- Blue Springs State Park with its manatees
http://www.floridastateparks.org/bluespring/- St. Augustine, historic town full of sites, worth 2-3 days alone.
West Coast:
- Tarpon Springs (Greek Sponge diving community)
- Sarasota and the Ringling Bros Museum as well as the Amish winter playground in the neighborhood of Pinecraft.