You guys have definitely hit one of my favorite topics. So be prepared for a rant...
I think I'm going to take the definition of "downtown" as put forth by University of Chicago Geography God (not to mention my professor), Michael Conzen. Conzen sees "downtown" as the most dense area of the city, with a concentration of office, entertainment, retail and public gathering space. It's where city becomes theater, shopping mall, and workplace all in one. So by this "technical" definition, downtown includes the Loop west to the Dan Ryan Expressway and south to Roosevelt (not Greektown or River West), the State/Rush/Michigan shopping and entertainment area north to Division Street, the residential district known as the Gold Coast, the South Loop to about 18th Street (including the Prairie Avenue Historic District), and River North up to Division and west to Sedgwick.
That area pretty much defines downtown in the "informal" sense for U of C students, as well. The four areas known to U of C undergrads outside their home neighborhood are "downtown" (basically refers to the places I mentioned above, and usually involves shopping, eating, or cultural activities), "Belmont" (which takes in all Middle North Side neighborhoods including Wicker Park, Bucktown, and Lincoln Park, and usually means shopping), "Up by Northwestern" (Rogers Park, Evanston, and Andersonville), and "Wow, that's far," which takes in everything else in the city limits with no apparent relation to distance. 44th and Pulaski (home of Pete's Fresh Market) is 40 minutes from Hyde Park, and is in the "wow, that's far" category, while the intersection of Clark and Belmont, 45 minutes on a good day, is not, and the answer to the question "Where will the new Hot Doug's be?" is "About two miles west of Belmont," which makes no sense to anyone other than Chicago undergrads.