The closest listing to Minneapolis is Willow River State Park, about 29 mi away. 6 places to camp sit within 50 miles, 14 within 100, and 42 within 150. Every one carries weather, wildfire proximity and a straight link to the official booking site, and the federal ones show live availability.
Federal campgrounds where the app shows how many sites are open tonight.
A lake, river or beach you can get into from camp.
The listing says pets are welcome. Leash rules are on each one.
Distances are straight-line miles from Minneapolis, not drive times. Mountain roads can double them.