Ali Baba has become my go-to for Middle Eastern fare in Pittsburgh.
I've ordered a few different things but the absolute best thing on the menu is the lamb shank, which a waitress recommended as their specialty. She was so spot on. The meat is juicy and fall-off-the-bone tender, and the tomato-based broth is seasoned perfectly. Yum! The salad is great (no surprise there, I'll eat anything with that lemony Middle Eastern dressing) and the kabobs and hummus are pretty good, but beware of the baba ghanouj...sometimes it can be very bitter if they make a bad batch.
The service is slow as hell, always. Not a quick eat, but satisfying if you have the time. Delivery is available through Wheel Deliver.