As you enter Minnesota on 35, you'll come to Albert Lea Mn. Right there, look for Helmer Myre Big Island State Park. Go to the White Fox campground. That will be a great place for you to park and drive around the area. Yes, the SPAM Museum over in Austin MN is worth the trip - it really is!
We camp at State Parks 90% of the time. In Minnesota they will NOT have full hookups but you can get electricity at your site. You will need to fill your fresh water tank and use it while camping. You'll need to dump your black/grey tanks on the way out.
If there is any way you could extend your trip, get up to the Itasca State Park in North Central MN. This is a great Park and also the headwaters of the Mississippi River. Then, head over to Duluth. Any of the State Parks on the North Shore (where Minnesota adjoins Lake Superior). Fantastic scenery on the North Shore drive. Then make a day trip North along US 61 stopping at the State Parks - especially the living history fur trading post at Grand Marais. Then head into Canada and visit Thunder Bay and experience Fort Wilkins. You won't forget seeing the trappers arrive in the birch bark canoes, the Indians in tents, the fur traders, etc. When ou head south, Check out the St Croix state park. Marvelous!