I have a summer house in Leland, MI north of where you are thinking of staying...there is NOTHING worth staying at between Chicago and the Inn At Bay Harbor. The american club is totally amazing but not on the water and if you don't golf its kind of a waste.
Inn at Bay Harbor is also in a better location in terms of summer activities near a better town for shopping/day trips etc

Good luck PM if you have any more questions...i know the area very well