How much time do you have and what time of year would this be?
If you have time to do something other than the quickest route, I would go from Miami
across the base of Florida and to the Shark Valley Visitors Center
of the Everglades, before I went on to Fort Myers
where you could visit Edison's winter house. Then go up the west coast of Florida to Tampa
and then to Pensacola
before heading up through Mississippi to Memphis
At a leisurely pace - stopping to see stuff like the Naval Air Museum in Pensacola or Fort Conde in Mobile this will take maybe 5 days although it is only 21 hours of driving. On the way back, head east Birmingham (Alabama)Atlanta
and certainly stop at Savannah
for a day and then head down the east coast of Florida to St Augustine
and Daytona Beach
. This is less driving time (15 hours) but there are more big cities on the route which take more time.