The Michigan Department of Natural Resources report that increasingly, pets are joining humans as they vacation in the beauty of our state's campgrounds, most of which are pet-friendly, as are most harbors, state forests and trail. There are some exceptions, such as state buildings, though presumably service animals are exempt.
While the DNR welcomes your family's companion/s, they wanted to remind us all of a few guidelines:
Pet Rules
 
First and foremost, any pet owner should be familiar with pet-friendly rules in state parks:
 
  • Pets must be on a 6-foot leash and under your immediate control at all times.
  • Always clean up after your pet.
  • Keep pets from interacting with wildlife.
  • Keep pets from disturbing visitors.
  • With the exceptions of locations included in the pet-friendly lodging pilot program, pets are not allowed in state buildings, which includes cabins, yurts, offices, teepees and lodges
 
It's also suggested that you talk with your veterinarian about meds, microchips and current vaccinations before heading to the great outdoors for a vacation - and maybe check for emergency pet services near where you're staying, "just in case".