Turkish Airlines has two of their offices in Nigeria, they are:
Turkish Airlines Lagos Office: Plot 1, Wing B, South Atlantic Petroleum Towers, 2nd Floor, Adeola Odeku Street, Victoria Island, Lagos.
Turkish Airlines Abuja Office: Shop 8, Sheraton Abuja Hotel, Ladi Kwali Street Abuja, Nigeria.
You can call Lagos office on +234 1 2772230-31-32 or CALL CENTER: 01 277 1559 or call Abuja office via +234 9 291 6669.
Note: that you can travel internationally from both offices irrespective of the class of travel.