North FL is lacking culture but nails the natural. Good stuff will probably be out of the way though, namely St. George Island and Apalachicola which I am betting is too far west for your route. I pretty much stick to state parks when going around the state and you should check out Myakka River State Park which is 20 miles from Sarasota (should be $6 for a carload and this is the best place to see a skunk ape.) Silver Springs near Ocala might be worth checking out too, but it will have transitioned from private tourist trap to state park by then. St. Augustine is an ok couple of hours but nothing mind blowing. Ringling museum in Sarasota has its art and special exhibitions open for free on Mondays and is definitely worth seeing. For $25 a person you can also view the mansion and the circus museum which is supposed to be really good. I have never been here but friends have loved it and this is definitely weird FL
http://www.solomonscastle.org/ about an hour from Sarasota.