Itasca State Park is Minnesota's oldest state park, first established in 1891. Its main claim to fame is being the headwaters of the Mississippi River where people like to wade across the river at its beginnings. The park has over 100 lakes and 11 backpacking sites located 1 to 5 miles from a road. The North Country Trail also crosses the park. Of course I prefer to hike to the furthest site in for more privacy and didn't see anyone one the 3 days I was there even though it was July. It helps that it was a weekday.

Itasca State Park website

Itasca State Park Map