Way out in the middle of nowhere, and I mean NOWHERE, is the Toadstool Geologic Park of Northwestern Nebraska. You have to drive for 20 miles from the nearest real town of Crawford, and then you have to drive 20 miles on a gravel road. There's actually 2 roads in, but only one on the road atlas. The southern road passes near the Hudson-Meng Bison Bonebed (which we skipped) and the northern route is more through the Ogala National Grassland.
When you finally get there, you'll see this:
It's also a campground, and you pay entry by the honor system in envelopes. In the two hours we were there, I'm not sure we qualified to need a pass, but I did it anyway to donate to the maintenance. Not that there is much- no water, only a couple (nice) pit toilets. Not that I'm criticizing a lack of facilities, but it's a heck of a trip to get there, so make sure you are provisioned with snacks and water. I wouldn't recommend camping unless you are really into the rugged stuff or have a camper.
Onsite is an old sod house, which I was glad to find was not infested with wasps or anything bad. This is rattlesnake country, after all.
The girls, Miriam especially, we're not impressed and started complaining very early on. It was hot and dusty.
Shortly into the trail, you come across an agate deposit. There were literally lines in the sand of it, and chunks came up easily and also just laid around.
Then we headed into the more more rugged sections, and the whining from the peanut gallery increased.
Then it started to look kind of cool.
Next thing we knew, we were in a "totally awesome" moonscape that required climbing over rocks and skirting the edges of miniature cliffs. The kids instantly perked up and enjoyed the scenery.
The "cliffs" required care, but were never really high. If someone had fallen, maybe a bone could have been broken, but more likely just scrapes would have resulted.
The trail was marked by posts, which often you could not see the follow-on until you were right at the next one.
Some of the toadstool formations were large, and in many places you had to climb up to follow the trail.
Some toadstool clusters were positively cute.
Abruptly the trail came to an end. Even with the heat it ended too soon. I think it was about a mile hike, but it didn't feel that long.
"Relatively" nearby is Fort Robinson State Park, the Agate Fossil Beds and some other options on the Dawes County website. It's right up near the South Dakota border at the corner of the Badlands.