One more thought... as I said earlier, showers can be spotty across central FL. Just last year, we exited HS in an absolute soaking, blinding, downpour, but over by MK , the ground was completely dry.
Both coasts of FL are well within driving distance along I-4, so if it is raining on one coast, consider the other as an option!
East coast: bigger waves, slightly closer, grittier sand
West/Bay Coast: softer waves, WAY more shells, more wildlife to see (depends a little which beach though)
The one little catch if you head straight along I-4, is that the causeway to Clearwater gets bogged with traffic. You can spend an hour trying to drive the last few miles. Though it is a beautiful beach.
An easier beach to access that we like is called Indian Rocks. (though it could probably use a name change.) It isn't super fancy, but it has everything we like: a parking lot with reasonable rates and even some shade, a bathroom/changing room, an outdoors shower to wash off sand, and across the street is an absolutely amazing restaurant called Guppies. (It is classic FL seafood house; what Narcoossee's aims to be, but better and far less $$. If you go, try the crab+ guacamole dip and the soups, esp the chowder.)
Truly though, there are many great options along both coasts, if you can find one with decent weather.
Still one more very fun and unique option this time of year....see some wild manatees! There are many places to see them, I think on both coasts, but one free location right in Tampa is the Manatee Viewing Center owned by Tampa Electric. Manatees like warm, and the power plant discharges warm water. In addition to manatees, we also saw a ton of fish and spinner sharks jumping out of the water. The pier's outdoors, but the gift shop is indoors, and the walk to your car is short if it is raining.
I earlier listed multiple interesting east coast options.