Bass Pro Shops in Orlando is huge and probably worth visiting. They're obviously heavy on fishing, but they have a large hunting section and a reasonable selection of other outdoor gear. Towards St. Petersburg, Bill Jackson Sports is pretty famous too and has a wider range of outdoor gear. Towards Sarasota there's Environeers, a backpacking store that used to sponsor Trailside on PBS. In Clearwater there's Venture Outfitters, a newer backpacking store. There are a few military surplus stores around Tampa and probably Orlando, but they aren't as good as ones near bases with really large units. For some weird stuff, in Orlando there is Skycraft, an electronic junk store.
Attractions. There are the obvious Disney ones. I'm a big fan of Disney resorts and the high standard that Disney maintains, even in their cheapest resort hotels. Personally, we go to Epcot at least 3 times more than any other Disney park. They're about to start their annual international food festival, which more than doubles the number of "native" food offerings they normally have.
In Tampa, Busch Gardens is sort of questionable. We have season passes and go a few times a year, but for almost a Disney price, it's just not as high a quality. The Lowry Park Zoo in Tampa is highly rated and a much better value. Some of the animal experiences are pretty unique, like the manatee exhibit or hand-feeding giraffes or stingrays. I'm not a big fan of the Florida Aquarium or MOSI (Museum of Science and Industry) in Tampa, at least not for visitors. We have season passes to both of those and take part in some kids activities there, but for a one-time visit, they're not as impressive as other attractions.
Hiking in Florida is a little sparse. There are a lot of smaller parks for day hikes. We like Lettuce Lake Park in Tampa or Brooker Creek near Tarpon Springs, which are both pretty educational about the different Florida ecosystems. When we just started backpacking, we did overnights at Hillsborough River, Lake Kissimmee, and Myakka River state parks. Myakka is the only one that really has the size for a multi-day hike. If you even wanted to day-hike any of those, you probably need to call the ranger station and see how flooded the trails are.
We've never stayed there, but a few different friends love to car-camp at Fort Desoto park in St. Petersburg. It's almost getting cool enough to be bearable. We'll probably try it this winter.
Another pretty unique experience in the area is fishing off of the old Skyway bridge piers. The old bridge collapsed in 1980 and now the approach piers are used for fishing. Shops there rent tackle and sell bait, so you don't need to bring anything. It's pretty deep water and people make some amazing catches there, especially considering that you can drive out and park right where you fish.