Karanlık Kilise, or the Dark Church, a rock-cut church in Göreme, built in the 11th century and decorated with Byzantine frescoes. It’s part of the Göreme Open Air Museum, inscribed on UNESCO’s World Heritage List since 1984.
For pictures of the frescoes in the church taken in 2005, see http://www.pbase.com/helenpb/image/51226376 and http://www.pbase.com/helenpb/image/51227296 along with the interiors of the Apple Church. They’re amazing and worth looking at but I’m unable to post them here due to a technical problem.
National Museum of the American Indian, posted earlier.