The Plant Museum is great if you love history and architecture. Henry Plant and Henry Flagler brought the railroad to Florida and had grand hotels in several places in Florida.
The Tampa International Mall by the airport is a very nice mall if you like to shop. It has a Cheesecake factory and some other popular chain restaurants there too.
Not far away is the Dali museum in St. Petersburg. It is one of the best collections of Dali paintings outside of Spain.
Across from the Dali is the Albert Whitted airport in St. Petersburg, which is just a small executive airport now, but it had THE first commercial flight in the US. The terminal has a restaurant upstairs that is pretty good. I used to go there for breakfast or lunch sometimes.
St. Petersburg is lovely to walk around. The Vinoy hotel has a small room at one end of the lobby that has some history about the hotel and the area. There is an art museum aside from the Dali, also very good. The Chihuly Glass museum also. Oh, and Paciugo gelato is delicious right there in that same area by the water in St. Petersburg.
All the St. Petersburg stuff is walkable, with the Dali museum and nearby airport at one end and the Vinoy at the other, and everything else in between. You cannot see everything I mentioned in one day, too many things, but you can do 2 or 3.
You could go to the beach! Clearwater Beach is busy with people, white sand, shallow blue waters, and a pier. You can take a dolphin boat there. The dolphins love to play in the wake behind the boats, they don’t have to do anything to entice the dolphins except drive by.
An hour or a little more away is Disney, Universal, and Seaworld. Even if you don’t want to go into the parks, you can go to Disney Springs (free parking) and go shopping, listen to the music in the evening, go to the restaurant Ragland Road and watch the Irish dancers (you don’t have to have dinner there, you can just go in for a bit and sit at the bar and watch the dancers).
Lakeland, FL is home to Florida Southern College which was designed by the famous architect Frank Lloyd Wright. They have a one hour and two hour tour, I recommend just the one hour.
You could drive an hour and a half and see where I live. Probably too far to bother. 60,000 golf carts driving around, restaurants, live music and dancing every night in the town squares. $2 boat ride with tall tales about The Villages. Also, Eisenhower Recreation center, which is like a museum. It’s free. Our residents donated memorabilia from WW2 to put on display.
If you are here now, in September, it is one of the hottest months of the year, stay hydrated and get some air conditioning every so often. This time of year you can expect daily thunderstorms between 3:30 and 6:30, they usually last about 40 minutes. Check the HOURLY weather, I like the accuweather app. Over 60% chance in an hour, and it will rain that hour. Below 50% it probably won’t, but this time of year the percentage can go up or down within a few hours. Outdoor activities will stop when lightning gets close. At Bush Gardens outdoor rides will temporarily close, pools at places like the YMCA will temporarily make everyone get out of the pool. etc. Lighning is no joke in Tampa it is the lightning capital of the country, go inside. Do NOT stand outside and watch the storm roll in. Especially if you are by water. If you are coming in a few months the weather will be very different.