Travis,
Personally, I just recently made a long weekend trip to the salt. I made the run to the Destin, FL area. Which has got to be the shortest trip since it's nearly a straight shot south. It was an easy 7hr drive (though you could probably make it sooner if you had to and were a little heavier on the gas then I was). It was my first trip to that area, but it won't be my last.
Redfish are available year-round. Jacks are available off of the beach in spring along with sea trout in the bays. Tarpon in the summer months. Off-shore is also not that far off-shore in the summer - sails and mahi mahi.
They just recently expanded the Panama City, FL airport. Southwest will start running a couple of direct flights daily starting in May (1:15min - 1:30min), if flying is another option. Though once you start flying that opens up a whole lot more of the coast.