We lived in Pittsburgh for 8 years. Our fave restaurant *hands down* is Road to Karakesh, an African-inspired restaurant. It's totally off the beaten path. The front of the restaurant has floor seating where you sit on pillows. It has a Moroccan theme inside. Everything on the menu is delicious!!!!! Its sister restaurant Spice Islands (Asian food) is down the street a couple of blocks and is equally yummy. Fajita Grill is also one of our top faves! It's Mexican food but has a lot of unusual dishes that you won't find in most Mexican restaurants.
Oh my gosh, my mouth is watering for my fave restaurants.
ETA: I forgot to mention that all 3 restaurants are BYOB! (They have a corkage fee, though.)