Middle Eastern in River North, Lincoln Park, Bucktown?
A short hop from your named neighborhoods, in Roscoe Village, is a wonderful Turkish restaurant, Turquoise, www.turquoisedining.com. If you interested in taking the Brown Line to Kedzie, there are great Middle Eastern options within a block or two, both restaurants and bakeries.
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.