There are so many guys who post here who can give you all the info you need, and you could probably play great courses there every day for a year. There are a number of excellent public courses scattered around besides Cog Hill. From a private standpoint any of the following would be awesome:
Chicago Golf Glen View Rich Harvest
Medinah Ontwentsia Black Sheep
Olympia Fields Shoreacres Butler
If you haven't been to Kohler you should give serious consideration to going there. In 1 1/2 days you could play Whistling Straits, Blackwolf Run, and maybe one of the others and stay in the less expensive annex building one night.