Indiana Dunes NATIONAL Lakeshore has a campground that, I believe, is all "primitive" (no hookups). I haven't been there so I don't know anything else about it.
Indiana Dunes STATE parks' campground sites all have electric, but no h2o.
The national lakeshore has some very nice trails.
I like the Willow Slough idea, but I found this on the website:
Camping
Camping, picnicking, and open campfires are allowed in designated areas only. Unloaded firearms, unstrung bows and arrows, and air guns may be possessed, but not used in camping and picnic areas. All weapons must be stored or carried in a case, or locked within a vehicle while in these areas. No swimming is allowed.
Even with a LTCH?
With an LTCH you are good to go. I'm going to call this morning, we plan on going 4/20 weekend.
Edit: I just got off the phone. It's $5 a night in off season and $12 after may 1st. No running water or toilets in the off season. Asked about carrying, her exact words: "we've never really had a problem with that, so we don't really enforce it."