No love for the Chicago District? Tho I certainly haven't played all of these, and am not certain as to where they line up in terms of position, I think we could put forward a pretty strong lineup of places to play (listed alphabetically and not in terms of strength):
Barrington Hills, Beverly, Black Sheep, Bull Valley, Butler National, Butterfield, Cantigny, Canyata, Chicago Golf, Cog Hill #4,Conway Farms, Edgewood Valley, Evanston, Exmoor, Flossmoor, Glen Oak, Glen View, Kemper Lakes, Knollwood, LaGrange, Medinah, Merit Club, Midlothian, North Shore, Northmoor, Oak Park, Olympia Fields, Old Elm, Onwentsia, Pine Meadow, Rich Harvest, Shoreacres, Skokie. We can even steal a few from other states (Dunes, Lost Dunes, Long Beach CC and Point O Woods are all in the Chicago District).
How's that for 10 minutes and overall depth? Mostly private with a few public access thrown in. I think we at least get into the discussion.