Here are a couple links to start with, anyway.
The only place that I know rents bikes is Orlandobikerental
. You can rent a hybrid for $30, but if you can spend $50, you can get a road bike or a recumbent trike. They are directly on the West Orange trail, which is a nice 50 mile round trip MUP.
is a map of the state with links to lots of other shops. I don't know which others rent. There is one shop right on the Pinellas trail in Tampa that rents bikes, but I can't recall which one it is.
Speaking of trails, here is a link
to many rails to trails MUPs accross the state.
If you like historic buildings, you should drive an hour north when you are in Daytona, and see St. Augustine. Good luck, and have fun. I hope you get some real Florida weather by then, not this 40 degree stuff we're getting right now!
p.s. Tour suggestions--I don't know how far you want to go, or if you are focused on riding or sightseeing. The Pinellas Trail in Tampa (about 70 miles round trip) and the West Orange Trail in Orlando are both decent low auto traffic rides, with lots of chances to stop and shop or eat.
The Van Fleet Trail, between Tampa and Orlando, is a wonderful straight flat ride, about 60 miles round trip, with little traffic of ANY kind, but bring your own supplies. The Canaveral National Seashore/Merrit Island Wildlife Refuge has miles of very low traffic roads, with lots of birds, snakes, and gators to see, if it's warm enough. It's about 50 miles or so to see it all. Again, you need your own supplies out there.
If you want a big ride, try circling Lake Okeechobee on the LOST trail, about 100 miles all the way around. That's about an hour south of Orlando. There are lots of places to camp and fish there, if you are into it.
There is also good road riding along most parts of route A1A near the ocean from Jupiter to Cocoa, and along the inland coast of the Indian River in St. Lucie and Cocoa.