I would recommend touring around Florida, in two months you have time to see the entire state.While it has a reputation as being cycle unfriendly, in reality it has gone a long way in making itself more hospitable in recent years by building entensive bike trail networks in and connecting remote regions(to encourage eco-tourism) as well as paths and lanes in the urban areas.I would recommend a bike equipted to handle rail trails as well as dirt roads and levees as this is a key to getting between regions and particularly getting around the Everglades and southern part of the state where an extensive paved backroad network is limited.

I am not real familar with the Panhandle but the southern tier route does cross this region and it is generally less populated than other parts of the state.The Big Bend area(ie around the Suwannee R.)has an entensive network of cycle friendly backroads as does the central region around Sebring/Lake Wales.Connecting these two regions are the James Van Fleet and Withlacoochee State bike trails as does US 27 with a wide shoulder though high speed 4 lane traffic.South from there you can ride 110 miles around the paved/dirt levees circling Lake Ocheechobee .From there you can continue south into the Everglades region either on 27 or turner road(dirt) or even levees.For info/maps on the entensive levee network in the glades see the South Florida Water Mngt District website and for info on turner road see the Big Cypress Natl Preserve website.

Besides US 27 the other major road through the Everglades is Tamiami Trail(US 41) which has a wide shoulder from the outskirts of Miami out to the Big Cypress eastern boundry.Fortunately you can take loop road a dirt road looping southward through the preserve from there and connect with turner road(another dirt road) which will take you clear up into the Lake O backroad region.You can also head south from 41 on 997(or Homestead backroads) bypassing Miami and reaching the main E.N.P. entrance and then further south on into the Keys.

Here is a route around SouthFl connecting the Keys and northern Everglades: http://www.floridabicycle.org/messen.../winter038.htm
I do not recommend the eastern urban part unless you like riding in heavy traffic but the east/west route is noteworthy because there are few onroad east/west routes across SouthFl(due to the contraining effects of the vast swampy everglades).Here is a tour using this route: http://www.stubna.com/cycling_florida/

And as was said above a route along the east coast beaches following A1A and US 1 is doable as well. These are the areas I tour so if you decide on this option I can give you more detailed info/resources particularly levee/dirt routes through the glades.