It's a little out of season, but still quite busy. Most of the "Florida" stuff is probably not open, yet. If you've got the bucks for it, a day trip of fishing in the Gulf would be worthwhile. Destin (just to the east on US98) is the charter-fishing captial of the Universe.
Eglin AFB has a nice
museum, there're many aircraft on display outside, and much more to see inside. You'll probably pass it on the way into Ft. Walton from the airport, look for an SR-71 and a B-52 on your left as you ride into town. From Ft. Walton, go up state road 85 north through Shalimar, there'll be signs.
If you haven't been to gulf coast beaches you'll be amazed at how clear the water is (yet quite cold this time of year) and how bright white the sand is.
For mobility there will be scooters and stuff, but they probably have restrictions on where you can ride. For a little more $$$ you can probably find real motorcycles, but there may be that 25 thing again for those. Also, for real motorcycles you have to have an endorsement on your driver license, even if from out of state.
Ft. Walton's not really a "touristy" place in the same vein as Destin or Panama City Beach, so as for stuff to do, it's not much different than any other town in the country, until you get across the bridge onto Okaloosa Island, and that's mostly hotels and condos. There's a marine animal park there called
Gulfarium that's probably worth a visit. It's no Sea World, or even on par with
Gulf World in Panama City, but it's a good place to spend a 3 or 4 hours.
Going east towards Destin you travel through
Gulf Islands National Seashore which is an area of pristine undeveloped shoreline, shaped only by a few recent hurricanes and the occasional Air Force facility. (The hurricane damage is in the form of flattened dunes with bare, grass-less areas, dead trees, etc.)
Panama City (my own humble abode) is about an hour east, Pensacola is about an hour west. (By car, not by bicycle!) Panama City will be starting into full
Spring Break mode by then, when the high school and college kids invade from all over, and the Canadian winter guests take flight (in their fleets of Buicks and Grand Marquis's) and migrate back home.
If you are into military museums, the Pensacola Naval Air Station has the best
air museum in the southeast, one of the best in the country. Navy-oriented, they have restored aircraft from the earliest 1900s to F-14s and F/A-18s, including WWI and WWII aircraft from both sides, early jets, and current aircraft. They also have a dirigible display, a section made up like carrier interior spaces, and a WWII jungle base. There's a simulator at the back of the main floor where you can go in and fly air combat against other patrons, then attempt carrier landings. This is no "ride," it's real F-14 simulators used in pilto training. (Costs $25, includes a training session and 20 minutes of stick time.) Their restaurant (sandwiches, burgers) is made of memorabilia taken from the Cubi Point O-club when the U.S. left the Phillipines. Also an IMAX theater, and be sure to take in the outdoor tour. That museum is a day trip easily. And free (except for the theater and the simulators.)