Although the entrance fees may be quite steep (around $30 for everything), Topkapi Palace is a must-see. This gem from the Ottoman Empire contains stunning architecture. Of particular interest is the tile work which is still in great shape. Take your time exploring because there is a lot to see. Be sure to tour inside the Harem. Outside, you'll facade of the Castration Room breathtaking. There is also a peaceful fountain in the back.
The Palace is closed on Tuesdays. Otherwise it open from 9 A.M. to 7 P.M. You can purchase tickets by the entrance to the Harem. You can find more information and even take a virtual tour on the official website: http://www.topkapisarayi.gov.tr/