On a clear day you can see the gulf from the top floor of the Capital building. There is the Florida Museum of Natural History behind the capital downtown and takes you from prehistoric Florida thru today. They have changing exhibits, but of course the endless displays of Spanish gold usually get most peoples attention.
Near the airport is the Tallahassee Museum of Natural History (formerly the Tallahassee Junior Museum, changed because people thought it was a petting zoo). The place is amazing, you walk through the zoo area in the animals natural habitat on board walks. It's one of the few places to see every kind of Florida wildlife up close. They also have a working village circa mid 19th century and restored homes including Prince and Princess Murat's originally Tallahassee home.
Also downtown is the art museum and science musuem about one block from the Florida Natural History Museum. The science museum is more geared towards kids, but seriously who can pass up interactive exhibits?
There is also a historical walking tour of downtown. The pamphlet is available at all sorts of places, but the capital is the only one I remember. It was created by my friend Andy Ashler for his Eagle Scout Merit Badge and has tons of information.
There's always FSU, if you go to the Alumni building they will give you a pamphlet that explains the history of many of the buildings on campus. The East end of campus is the old part and has buildings dating back to 1851. If you can, go see the old Dining Hall and Montgomery Gym they have both been restored to their original look and are incredible. You probably won't be able to get into Landis Hall, but it is overlooking Landis Green and a Public Works project from the Great Depression. It is truly a work of art and has some amazing wood work and masonry.
If you plan in advance you can get tickets for a tour of the governers mansion and is quite an interesting tour, however the true time to go is after Thanksgiving when the christmas decorations are up.
If you're headed back to SoWal you can head south from the airport and hit Wakulla springs. It's one of the oldest nature preserves in the world and true beauty. Take the glass bottom boat tour and then have a quick bite in the Lodge.
