The Aiken-Rhett house/museum is a great house to tour, whether you live in Charleston or are an out-of-town guest.
Most of the house is in it's "original" (read: not yet restored) condition, in that the Historic Charleston Foundation is still taking wallpaper and paint samples to (I think) eventually restore it. So don't expect glamourous, just think "historic".
You will receive a walkman with a 45-minute taped tour that takes you throughout most of the house, as well as the grounds and the slave quarters. It's quite interesting, even for someone like myself who is bored by history!
If you plan to visit the Historic Charleston's other house (the Nathaniel Russell house), make sure to visit that one *second*--as it is completely restored and is a nice contrast to the Aiken-Rhett house.
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