I agree with Jack's post. Other options are US1 Daytona South to Oak Hill, and take SR 3 through the Space Center National Wildlife center (if there's no launch pending), then A1A (congested, but beachy) South to Melbourne, then West on 92 @ Melbourne and then South on 441 (no towns or traffic) to Lake Okeechobee. Circle the lake either side, then 27 south to the Turnpike or Sawgrass Pky. Getting away from the coast will show you a more rural Florida.
On the way back, US1 into Coral Gables then to A1A is worth a few hours. South Beach and all that stuff. I did it ONCE.
If you don't already have a place to park your truck & trailer, I'd suggest trying a business with a fenced yard on Nova Rd. which is west of US1. Some will let you park for a fee.