Must-see Florida towns

Depends on your interests but this is what we've enjoyed having visited for many years:

Crystal River is a must if you want to swim/snorkel with the Manatees. We go out with a company called Birds Under Water around 6.30am although there is a later time. Venice is a cute town on the gulf side, The Jetties At Nokomis we enjoy and provide fabulous sunset viewings, dolphin and manatee sightings. St Armands Circle, Long Boat area. Two Jack Marina Area Sarasota pleasant walk around especially evenings. Anna Maria Island, Cape Coral, Naples.

On East Coast we generally enjoyed, walking around Fort Lauderdale (Also good Mall there, Sawgrass?), especially close to the waters, and various parts of Miami to experience the diversity of communities, flora and fauna - Little Havana, Coconut Grove, Coral Gables, South Beach, Key Biscayne, Boca Raton, Palm Beach, and nice to stop at lots of the smaller beach towns as you go up the coast north of Fort Lauderdale.

If you enjoy/able to Kayak, there's truly wonderful kayaking for miles around Estero,(Great CalUSA Blue way - shoreline, mangroves and more) but if you want to rent a small pontoon or boat for half day/full day to explore, SaltySams Marina in Fort Myers area worked well for a group of us varying ages and abilities.

Have a fabulous trip.

We made that trip in 2014. Spent a couple of days in Ocala visiting friends. From there went to Fort Myers beach. Stayed at Red Coconut, visited Sanibal island. Then we headed to the Keys. Stayed at Jolly Rogers campground in Marathon. That was about halfway on the keys. Visited almost all of the islands. Spent most of the time at Key West though. Then headed up the Atlantic coast. Made a stop in Orange to see relatives. They took us to Blue Springs but did not see the Manatees. From there went to Fort Pierce for a few days. Traveled back and forth to Daytona Beach. This is probably the nicest beach we ever been on. Then on to Jacksonville to visit a friend before heading back North.
Should have made a few more stops but needed to get back home to get the RV worked on before warranty ran out.

Stuart, Key West, Naples

West Coast: Cedar Key, Manatee Springs State Park, Rainbow Springs State Park, Tarpon Springs, Sarasota.
Everglades airboat tour and Ah-Tah-Thi-Ki is a museum of Seminole culture and history, located on the Big Cypress Indian Reservation.
East Coast: Kennedy Space Center Cape Canaveral, Daytona Speedway and museum, St Augustine.

Since you said the gulf coast, I would include Pensacola and Applachicola.

Apalachicola
Carrabelle
Cedar Key
Old Homosassa
Chokoloskee (take the toad from Midway CG at Ochopee)

There are old-Florida laid-back places.

How long do you have? What interests do you have?

You literally could spend a year exploring all there is.

It is a big state.

Cedar Key, Crystal River west coast.

Flagler Beach east coast.

West Coast Notes:
The "Sunday Sunset Drum Circle" on Siesta Key Beach (sugar white sands) near Sarasota is a happening to experience at least once.

Pier 60 on Clearwater Beach celebrates sunsets in style every day.

x2 on Tarpon Springs- there is also a dessert/bake shop down at the docks that is out of this World.

St.Augustine, Cape Canaveral, South Beach Miami, Marco Island, Sanibel/Captiva Island, Fort Myers Beach/Estero,the springs in the Ocala area(Juniper, Silver Springs), Anna Maria Island, Key West, Mount Dora, Everglades, Naples, Tierra Verde(Fort DeSoto), just to name a few :)