The Chora Church is located in the outskirts of Istanbul and, while it's a ways away from the city's main points of interest, it's still a must if you're traveling to Istanbul. The church was built in the 4th century and subsequently rebuilt over the years; the current incarnation was finished in the 9th century.
It was originally a Christian church which was converted into a mosque once the Ottomans took control of Constantinople. It had beautiful frescoes on the dome and interior walls but they were painted over and a minaret was added. The church also has several smaller chapels which give it an irregular shape (a fact which is easily appreciated once you reach the rear of the church).