Well, this is very interesting. I did a deed search and matched stated owners as shown on the GIS property mapping, found liber numbers, with any deed activity such as warranty, quit claim, etc.
Here is the situation as I see it: the area known as "the fairgrounds" is composed of 7 different properties with 3 different owners: The Ionia Fair Association, the DDA, and the City of Ionia.
If you were to take a map out and look at the fairground, you notice that the DDA owns property in the North side of the property bordering West Main. Since this property is owned by the DDA (Ionia Downtown Development Authority) and the CDL seems to indicate preemption applies to authorities created by local units of government, you most likely could possess a firearm on property just south of West Main.
Now, looking at any entrances one could actually use to access the fairgrounds, "The Ionia County Fair Association" is listed on deeds as the owner. This also includes about 90% of the remainder of the property. HOWEVER, the post above is correct about the city owning the property under the grandstands. If you imagine a rectangle shaped of property with an "island" of city property under the grandstand, this would be fairly accurate. (There were a few feet off of a perfect square here and there) Therefore, although, you could carry in some areas because they are city owned, you would have to cross, at a minimum 50 feet of Fair Association property.