The Kariye Museum (Church of the Holy Savior in Chora) has the best Byzantine mosaics in the region. If you can spare two hours, you must see them.
Originally built in the 4th century as the 'Church of the Holy Savior Outside the Walls' or 'in the Country' (chora), it was indeed outside the walls built by Constantine the Great.
The building you see was built in the late 11th century, with lots of repairs and restructuring in the following centuries. Virtually all of the interior decorationÔÇöthe famous mosaics and the less renowned but equally striking mural paintingsÔÇödates from about 1320.