Although this church may look a bit worn-down, especially on the outside, it still has a lot of heart. You don't need a tour guide to enter and if you don't want to pay for one then ignore the touts around the entrance.
The Church of Holy Wisdom was originally constructed in Roman times and contains Byzantine architecture. Parts of the building periodically collapsed. The church was made into a mosque following the conquest of the Turks, and you'll see lots of hanging examples of Islamic calligraphy. Be sure to look up at the very tall ceilings; you don't want to miss all of the little touches. Take your time exploring this vast church/mosque/museum and keep in mind that you can explore the second floor.