I suggest that no “town” is particularly fun, but the beach communities for one are more fun. In particular, Tampa itself is pretty much dead at night.
For Jacksonville, the areas of interest are Amelia Island and the Jacksonville Beach area. The coast of this part of Florida is a kind of windswept beach, long stretches of soft sand.
For the Tampa Bay area, you want to look at Treasure Island, Indian Rocks, or even the Clearwater beaches. Here the beaches are powdery white, the water is more of a turquoise blue.
In both places you have bars and clubs in the beach communities. At this time of year, the Tampa area is warmer. The water in the Gulf of Mexico is currently hovering around 70 degrees near Tampa.
I suggest the greater Tampa area would be the best choice.