New York (Manhattan) is the only American city I can think of in which "downtown" is widely recognized as a direction rather than a destination. In most other large American cities, downtown is the central business district, containing large office buildings as well as major hotels and transportation hubs. Most of those neighborhoods called "downtown" are smaller than a mile square.
The corresponding neighborhoods in Chicago, more specifically those that are walkable from the major hotels and transportation hubs, can include the Gold Coast, Magnificent (not Miracle) Mile, Streeterville, River North, Loop, West Loop, and South Loop. These neighborhoods extend up to three miles from north to south.
Many of the people who ask about "downtown Chicago" are from out of town, and don't realize that the relatively compact "downtown" they're accustomed to back home covers a much broader area here in Chicago. They don't realize that restaurants within walking distance if they're staying "downtown" at the Ambassador East are entirely different from restaurants within walking distance if they're staying "downtown" at the Hilton on South Michigan Avenue. So to me, as someone who has lived here for decades and is familiar with the area, the term "downtown Chicago" is very non-specific; when someone asks for restaurant recommendations in "downtown Chicago", I often reply by asking them to be more specific about exactly where they're staying or spending time.
In the context of our discussion here of a "comfort burger" (which as far as I can tell is what I would call a "hamburger"

), all of the recommendations made here, with the exceptions of Monk's Pub and Epic Burger, are within a few blocks of the Magnificent Mile, which sounds like what the OP is looking for.