Great hike and camping spots going up Black Elk Peak, formerly Harney Peak. Plan the water and camping spots, great views from the top.
As others have suggested, Porcupine mountains and Isle Royale are both excellent choices: similar, but different than SHT.
A couple comments: If you go to Isle Royale, I would suggest bringing a minimal go-to-ground backup (i.e., at least a minimal pad) along with your hammock. This is because the park service is pretty strict about camping on the actual camping pads, and not going off into the woods even a short distance to string up a hammock. I was able to legally hammock for 6 straight days there, but if the place had been busier I could certainly imagine having to go to ground. Compared to SHT, Isle Royale doesn't have the rapid rivers and falls, but it has more of a sense of true wilderness, and yet still mostly well maintained trails. It also has it's own discussion board: https://isleroyaleforums.com/
Closer to home, there are North Country Trail sections in Wisconsin and west/central MN. I am familiar with the MN parts: nice trails, but much tamer terrain than SHT. Not much for overlooks, but some very nice camp spots on backcountry lakes. Also, surprisingly remote: you can pretty much hike from a trailhead just east of Detroit Lakes, all the way to near Remer east of Walker; you will cross roads, but pretty much never see any houses or other buildings. I have frequently (not always) had a campsite to myself, even on a saturday night.
Others have commented on South Dakota hiking, so I will comment on North Dakota hiking. Believe it or not, there's actually a really nice area for a 1-2 night hike, which is the north country trail through the Sheyenne National Grasslands in SE North Dakota. Again, the terrain is tame (there are microhills, not real hills), but it's a mix of open prairie interspersed with hardwood forest groves that make great hanging spots; it's really a much more open, "western" feel than you get in minnesota.
Think at the moment I am leaning towards a Porcupine Mountain trip and then either the Kekekabic or Isle Royale. Really appreciate all these great ideas!
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