The Travelin Man
Bern’s may be excellent, but Tampa is about a four hour detour from FLL to St Augustine. Tampa is on the west coast, while the drive from FLL to St Augustine is straight up I-95 on the east coast.
Also, Clark’s Fish Camp (also excellent) is a little farther than "just outside" of St Augustine. It is about a 45 minute drive from downtown St Aug to Clark’s.
On the other hand, the shrimp are excellent, as was this dessert (deep fried cheesecake):
On the other hand, the drive will bring you right by the legendary Dixie Crossroads in Titusville (also a quick stop right off I-95).
If you wanted to take a detour out to towards Kennedy Space Center, there is a solid Cuban place over in Cocoa Beach named Roberto’s Little Havana.
For more suggestions, search using some of the cities on the route you are traveling: West Palm Beach, Melbourne, Cocoa, and Daytona Beach for starters.