Think about the kinds of public lands in your area that already have geocaches. What are they? City parks, county parks, national forest, state park? Has a city, county, Chamber of Commerce, Convention and Visitors Bureau, or the like sponsored a geocaching event?
The Michigan Geocaching Organization has information on known land use policies on their web site.
Are there any areas near you where geocaching is allowed that do not yet have a cache? Is there perhaps a large park that would support another cache?
Are these places at least .1 mile from the nearest cache?
When you have a few potential locations in mind, I would advise, go take a look, and keep an eye out for spots that could support a cache. You may find out that one trail is too exposed, or that one park has no good hiding places, but you may find a pleasant area that you never knew about.
Unless you have an extraordinary container in mind, I'd recommend choosing a container that fits the place and not the other way around. Take measurements. Note coordinates.
Prepare container. Place cache. Take coordinates again. Average coordinates (the more readings on different days under different conditions, the better). Submit listing. Cross fingers.