To get a little further away from civilization, you can also camp at the end of the Root Glacier trail, about 4 miles from Kennecott. This is hardly a traditional campground; there are a few creative spots to pitch a tent, one of which is on the trail itself. There's also a bearproof food storage box, since this is definitely bear country. But few people and amazing views make the hike out here worth it. You'll know you're at the end of the trail when you're just past the cables coming down the mountains from the old Erie Mine. Be careful if trying to access the glacier from this area. Your best chance of doing it safely is by backtracking to finding a grassy ramp; otherwise, most of the rock on the sides of the lateral moraine will come down with you.
Trail to End of Root Glacier