Istanbul's fine Carpet Museum(Halı Müzesi) is within the Hagia Sophia (Ayasofya)complex. You enter by the grand, ornate Ottoman Baroque doorway at the northeast corner of the complex on Soğukçeşme Sokak near the grand entrance to the First Court of Topkapı Palace (map).
Lodged in the beautifully-restored former İmaret (Dining Facility, built 1742-1743) of the Ayasofya mosque complex, it consists of three exhibit halls: the former dining hall(me'kel),kitchen(aşhane), and bakery(fodlahane).
Eastern Anatolian carpet,
You pass from one hall to the others through electronically-controlled double doors that preserve the environment for the centuries-old carpets on exhibit. As you examine the carpets, take a moment to also examine the restored halls. Important features have plaques explaining their functions.