Anatolia Cafe is my favorite place to go to for Mediterranean food on the east side of Cleveland. It's a restaurant that I frequently visit and recommend to my friends.
The doner (slices of beef and lamb) is advertised on the menu to be the best in town. I haven't tried all of the doner in Cleveland, but of the ones I've tried, it is my favorite. I've ordered this dish the most when I go to Anatolia. I've recommended this dish to five of my friends, and they've all agreed that this dish is really good. Delicious and not gamy.
The other meats are good. The doner is the best, but the filet mignon cubes in the beef saute are also worth a try. In my opinion, the portions are medium sized. They are reasonable, but if I am going to dinner hungry, I need to also order an appetizer to be completely full. I would recommend one of the cold dips - I've tried and liked the hummus, baba ghanouj, and the eggplant with sauce.