The easiest way would be head north on the ACO's Atlantic Coast Route until you reach St. Augustine and then head west on the ACO's Southern Tier. I like riding throught the Ocala National Forest (hot springs) to Ocala. You can also take Rts 26 and 40 west to Gainesville, from Palm Coast. If in Gainesville eat at Satchels, the best pizza and salad!!!!! I believe, from Gainesville, there is a railroad trail (to St. Marks) that might get you closer to Tallahassee. I road out of Tampa to Ocala then via Palatka to St. Augustine, last summer, a very nice trip.
Interesting - I am actually starting the Southern Tier but was looking at options for getting to the starting point in St. Augustine with my large Trike. That's why I was looking at Daytona Beach as a starting point. Having to fly into JAX and somehow get to a St. Augustine hotel near the beach seemed problematic. I suppose that I could just ship it ahead to my hotel. So you think the ACA route is the best heading northwest from the east coast?