In Tallahassee:
The Tallahassee Museum is a local favorite for kids. It is a small refuge type zoo/museum for native Florida widelife.
Wakulla Springs is one of the deepest springs in the world. The boat tours are highly recommended!
Near Tallahssee:
Thomasville, Georgia is a great place for antique shopping and that small town Southern charm. It's about 30 minutes north of Tallahassee.