Middle Eastern in River North, Lincoln Park, Bucktown?
Those areas in general, but if you have other ideas...
There's a wonderful Indian/Nepalese restaurant on Milwaukee Avenue in Bucktown/Wicker Park. I know it's not technically Middle Eastern, but it shares some culinary sensibilities. I've even had them cater a party.
River North has quite a few Middle Eastern restaurants, many of which are well-attended by taxi drivers from that region. Some are better/cleaner than others. Of those I would recommend Kan Zaman on Ontario and Wells or Reza's on west Ohio St.