A few others for consideration, both public and private:
Spring Valley (Salem, WI) -- Another Langford/Moreau that has not been touched and an interesting foil to Lawsonia. Will take some architectural squinting to fully appreciate "what it could be" if the bunkers had sand in them and the greens were returned to their intended size. But nevertheless, the property is interesting, the greens are generally good and in some cases great, and an old course diagram still hangs above the naugahyde furniture in the bar.
The Kingsley Club (Kingsley, MI) -- Call the club, and I'm sure they'd be happy to accommodate a tour.
The Mines (Grand Rapids, MI) -- A true municipal course by Mike DeVries. Routed over rolling terrain with a very nice set of greens. Most interesting perhaps is the relative lack of bunkering.
Lost Dunes (Bridgman, MI) -- To see how an old sand quarry bisected by a major highway and fraught with environmental zoning issues can become a pretty decent course. Most people talk about the severity of the 4th green, but I recall Tom Doak himself stating that the 7th is one of the few that may have been borderline.
Bay Harbor (Bay Harbor, MI) -- To see how an old shale (I believe) quarry with amazing water views can be totally %$^&'ed up.
Dunes Club (New Buffalo MI) -- Just to both second Howard's rec, and clarify that it's in SW (not SE) Michigan very near Lost Dunes.
Battle Creek CC (Battle Creek, MI) -- I haven't seen it, but Doak listed it as one of his top 10 discoveries in a 2012 Golf Magazine article.
Arcadia Bluffs (Arcadia, MI) -- Like Whistling Straits across the lake, many on the board lambaste this course for having moved a ton of dirt during construction, manufactured quirk and being a challenging walk. However, I have always enjoyed playing its super-undulating greens and generally firm/fast conditioning. In any case, it's worth seeing so that you can form your own view -- and the adirondack chairs overlooking the 18th green would be a fantastic place to reflect on it and the other courses you visit.
Tullymore (Stanwood, MI) or True North (Harbor Springs, MI) -- If you either (i) love Jim Engh designs or (ii) want to understand why most people on the board do not, these are worth a look.