via naraeng2g.
Earlier this year a cafe called Cafeteria Pittsburgh opened in Seoul's Jongno-gu, in the basement of the Gran Seoul building that opened in 2014. Judging by a few blog entries that have photographed it (here and here), it's local in name only and specializes in coffees, juices, and bakery items. The address is 서울 종로구 종로 33 그랑서울 지하1층 (우)03159 (map).
A couple other businesses in Korea bear the Pittsburgh name: a bar in Siheung (경기 시흥시 은행로144번길 21-1) and a pizza place (경기 안산시 상록구 초당2길 14) in Ansan.
There was a pizza and hamburger chain called 더피츠버거 (The Pittsburgher), which is how "The Pittsburgher" would be romanized but is written PizBurger, a portmanteau of two primary menu items. It used to have locations in Seoul and Boryeong, but appears to have closed a few years ago.