If you plan to swim, March is going to be hypothermia territory anywhere north of Ft. Myers. I would disagree that Destin doesn't attract college students, though I grant it doesn't have the marketed Spring Break programs; kids from further west along the Gulf Coast states head there quite often (and often stay in the family's timeshare) and the presence of the military bases is hardly any kind of deterrent -- I remember quite well hitting those beaches in search of nice young Airmen to spend some time with, LOL.
If you just want beach, and not warm water, the northeast coast has quite a few quiet areas. Further south, Daytona Beach Shores is surprisingly quiet and normally quite affordable, especially if you don't mind crossing A-1A. (In Florida, except for in Miami Beach or Sanibel, you pretty much never have to stay far enough away from the beach to need to drive there unless you are really scraping up pennies. In most parts of Florida, the price of lodgings drops dramatically the moment you get on the inland side of the main beach road. In most of the quieter beach areas, that is easy walking distance to the sand, normally less than 1/4 mi.)