Most of the places I've boondocked in the UP are on private land that I can't get you access to, but here are a few ideas:
In Munising, there is a township park just west of town that has campsites right on Lake Superior - it's not a big time park, but the lake is literally ten or fifteen feet from the campsite. Very pretty.
Porcupine Mt. State Park is perhaps "typical" of Michigan state parks as to campgorounds, and the trailer sites are nothing to write home about for the most part, though one of the campgrounds has nice views out over the lake (I think it's the upper loop at the Union Bay campground ... but there are LOTS of long hiking trails, many short hikes to incredible views (especially in the fall), etc. If you're there and the colors are "on", don't miss the short walk to the view at Lake Of the Clouds.
If you go here: Michigan Park and Trail Map
you will bring up the DNR's interactive trail and campground map. Just click on a county and you will get a full listing of all the trails, state parks, and more important for your purposes, all of the State Forest campgrounds, which are rustic and have at best a water soruce and pit toilet. All along the north shore of the UP, these campgrounds tend to be on fishable rivers. And there are a LOT of them.
Consider looking in the Michigan DeLorme Atlas for all of the waterfalls along the Lake Superior shore ... each is on a river that flows into Lake Superior, and each waterfall is a.) accessible via some sort of hiking trail, b.) a natural barrier to fish getting farther upstream, and c.) near some sort of campground. A little prospecting will get you to some nice fishing.
In any of the State Forests, you can engage in "dispersed camping" and camp anywhere that isn't posted to the contrary ... go here for information: DNR - Dispersed Camping
There are two major "catches." First, you need a "dispersed camping" permit, which is a little two-part gizmo that the DNR puts out ... if you call them and ask for a dozen or so, they will mail them to you promptly - you can't get them online. Second catch is (if I recall correctly), you have to be 50 feet off of the nearest road, and that sometimes is a challenge, what with ditching, etc. But there are lots of places in the UP that you can do this.
Finally, as you may know, most of the out of the way places in the UP can be quite remote and very sandy, with the roads in various states of disrepair and damage from logging operations. If you don't have four wheel drive on your tow vehicle, I would be pretty cautious about getting too far off the beaten path: I've needed 4wd pretty regularly on some of those things that pass for "State Forest Roads" in the UP, and indeed have found some of them impassible even when not towing and even with 4wd. If you're going off the main roads, for certain take a good high lift jack, a come-along or winch, an axe or saw, and a shovel. There's nothing much worse than getting high centered an hour's walk from the nearest paved road. Don't ask how I know this. And if this were to happen while you were towing, you'd be there a long time.
But in a few weeks, the UP will be gorgeous and the trout still hungry! Sorry to be long-winded, but hope this helps. Enjoy!