We wouldn't travel outside the immediate area to go to a beach, because they are at least as good as any we know. 

But sometimes you want a change, and to go a bit further afield.  So here are some day trips that we have particularly enjoyed:

Visit the Ringling Museum, or Mote aquarium, and take a boat trip on Sarasota Bay.

Naples - walk on the pier, watching the fishermen and spotting dolphins.  Visit Tin City, or shop at Coastlandcenter Mall or Waterside shops, and maybe have lunch at Venetian Bay.

St Petersburg - visit St Pete's Pier or the Dali museum, and maybe go down to Fort de Soto's beautiful beach

The Everglades - drive down to Everglades City and Chokoloskee (and have lunch at the Havana Cafe - the Cuban hot pork sandwich is wonderful!), then take a boat trip round the 10,000 islands.  

Or go on to Shark Valley & take the tram tourTake an airboat ride on Lake Trafford, Myakka River State Park or in the Everglades

Spend the day on Sanibel & Captiva ... start at Lighthouse beach, walk around the tip of the island looking for dolphins in the surf, go to Ding Darling wildlife reserve & take the tram tour, then drive up to Andy Rosse Lane on Captiva & have a drink & maybe eat at the Mucky Duck, watching the sun go down