Not sure why you are going to Minnesota in June but if it is just a destination picked at random, I would suggest turning south and following the Rockies down to CO instead.
I spent Jun-Jul in Wilmer, Minn. one year and would not want to do it again.
ANYway, Rest stop camping away from cities has always seemed safe to me, but near cities they can be sketchy. I have never had any problems but I do take precautions. Never let wife or kids go out of sight/walk to bathrooms alone especially at night. Be very skeptical of anyone who approaches you. Drive away if anything does not seem perfectly safe/normal.
Truck stop RV parking areas are noisy but safer than rest stops near cities IMO. You may see some interesting sights but the people are not a threat.