From the folder you get at the museum: “The Kaleiçi Museum was inaugurated on the 18th of May 1996, after Suna and Inan Kıraç purchased two ruined buildings registered as “cultural assets under protection” in the Old City (Kaleiçi) of Antalya and committed them to an elaborate restoration […]. The museum is part of the Suna and Inan Kıraç Research Institute on Mediterranean Civilizations of [the] Vehbi Koç Foundation. “ It is housed in two separate buildings, one a former mansion, the other a former church dedicated to St. George. The latter houses a fine collection of mainly Çannakale earthenware (I don’t like it in general, but they have some pieces I appreciated a lot). In the mansion social life is shown with mannequins in costume.
I have been informed that the "mansion" in actuality was a small Greek monastery, which would much better explain the nearness of the church. My correspondent suggests the monastery may well have served as a mansion, for instance after Greeks were sent from the country in 1923.