1) Tallahasssee Fun Station - go karts, Arcade, laser tag, pizza, bumper boats, etc...
2) Mission San Luis - a large reconstructed historical site with live reenactors which has a colonial era Spanish fort and mission and Apalachee “Indian” village. Better than you would think and the reconstruction work is excellent.
3) Museum of Florida History - a small museum that takes 2-3 hours dedicated to Florida history with some prehistoric animal skeletons which will impress the kiddies.
4) Tallahassee Automobile Museum - a lot of cool old luxury and sports cars as well as batmobiles and batcycles from the movies and old tv show. It’s actually a relatively large museum.
5) Tallahassee Museum - relatively large zoo of native animals including two Florida panthers, with at least two ropes courses (one short and one long that is harder and more strenuous) that you and your oldest could do and there is a kiddie one I believe your youngest could do. There’s also art installations (including large dinosaur sculptures made from used car parts) and “pioneer” reconstructed villages.
6) Challenger Learning Center - typical small kiddie museum devoted mainly to Science with attached IMAX Theater with documentaries during the day and real movies at night.
7. Wakulla Springs - a little bit of a drive but the boat tour is usually worth it and you frequently get to swim with live manatees in the main spring (no guarantee, they come and go freely).