All of the things the previous poster mentioned are great. I grew up in Tallahassee, so I'm super familiar with the area. If you have any questions, feel free to shoot me a message and I will help you as much as possible.
Tallahassee is an available city on Groupon. That's a good site to get some good deals on things to do and places to eat in town.
Tallahassee is a big college town (Florida State) so there are a lot of activities surrounding the games, but also a lot of traffic issues. If you are in town on a game weekend, they have a Downtown Getdown the Friday night before the game at Kleman Plaza which is like a mini-festival with vendors, live music, and pep rallies. Sept 3 is the first home game, so keep that in mind if you're still in town for that.
Kleman Plaza is also home to the Challenger Learning Center/IMAX theater which has some neat things to see. There is the Junior Museum, which is good for kids. If you can, take a tour of the Capitol, especially if you can go up to the top of the new Capitol. You can see the entire city from there. Wakulla Springs was a fantastic suggestion as was the Leon Sinks. MoMos pizza is great and the pizzas are HUGE.