The state parks in the U.P. are very nice and you haven't mentioned what hookups are a must or what you will be camping in. For a CG, I have to assume that electric is a must and a min of clean bathouses and showers plus a dump station and having fresh good tasting water to refill your tank.
For a week stay with camping in one or any Michigan State Park, it's cheaper to buy the annual pass which is good for any of the over 100 state parks. Most state park CG's are about $22 a night for the site in the U.P. So much to do and see all over the U.P. and it will be much cooler than in MO. Bring a light jacket or a sweatshirt for at night as it can be in the upper 50's overnight and usually the mid to upper 70's and sunny during the daytime.
Tahquamenon Falls state park has 3 CG's and it's a gorgeous area. North of Tahquamenon Falls on Lake Superior is Muskallonge State park CG. Porcupine Mtns State Park is about 60,000 acres with the CG on Lake Superior. Indian Lake State Park at Manistique is real nice and there's the huge Palms Books springs a few miles away. Straits State Park at St. Ignace is great with 2 CG's and Mackinac Island and the huge bridge to the Lower Peninsula. Just a small spattering of the many state parks in the U.P. Gobs of nice CG's in the Lower Peninsula too just by crossing the 5 mile long very high bridge.
Some really like Aune Osborn CG in Sault Ste Marie, MI as it's right on the wide river next to the SOO Locks (the world's busiest locks) that has huge freighters passing close by every day.