This is the monumental church built by Justinan in the 7th century to be the church of all churches. After the Turkish conquest in 1453 it was converted to a mosque (hence the minarets) and the original Byzantine/Christian decoration covered up or removed. But in the 20th century it was converted into a museum and restoration begun to return it to what it looked like previously.
Why does Wife look so Imperial in this picture?
Because she's standing on the Empress' spot, the place where the Empress would stand during the services at the basilica.
We spent a long time at the Archeological Museum but most of it I didn't think was that photogenic. The Tile Museum however was the exception.