I am currently living in Michigan and one of my favorite day hikes is at the Pictured Rocks National Lakeshore in Michigan's Upper Peninsula. I have hiked this network of trails several times, and it never gets old! My all-time favorite hike is the Chapel Loop, a 10.4-mile loop that takes you past forest, waterfalls, and a beautiful beach and lakeshore.
If you are looking for a weekend backpacking trip, you could split this trail into two days and camp at one of the campgrounds!
Here is a link to a post that someone created about this loop.
Here is a picture of the map:
I market the typical route in green, but you can follow the trail I marked in red for a slightly shorter path. I recommend travelling counter-clockwise, heading out towards Chapel Rock first, then heading towards the Grand Portal Point and Mosquito Campground.
Hope you get the chance to explore this beautiful place!