Ryan Crompton
Google
This was an enjoyable hike in the chilliness of North Dakota.
To start with, many of the directions posted elsewhere are wrong. To get here, to east out of Amidon; after a couple miles you'll see a standard green highway feature sign with "White Butte - North Dakota Highpoint" posted on it. Turn right (south) here.
Take the dirt road for 5 miles. Turn right again (it's between the 4.9 and 5.0 mile mark). Take this road for about 1 mile. You'll see a mailbox and an oil drum to the left. This is the beginning of the access road. Unless you've got a 4WD with good clearance and the ability to get out of the mud, park here.
Turn left / south at the mailbox (either on foot or in your car). Keep the fence to your left at all times. That'll bring you to the gate in my photo after about 1 mile.
Go through the gate (and close it behind you), and you'll have about 3/4 of a mile of hiking to get to the summit. In winter, this is a mix of crusty ice, snow, bare ground, and scrub brush, so pack accordingly. We summitted on March 4. Microspikes are probably advisable. There's something like 400-500 feet of elevation gain depending on the route you take. In summer I'd imagine this is probably a walk-up, though in winter it's going to be a little more challenging.
We stayed at Cabins of Amidon, which is run by very friendly people. Throw back a couple Hamm's at the bar next door while you're there. I don't know that I'd go out of my way to hike this route, but if you're a highpointer it's going to be on your checklist anyways - and it's a mildly interesting hike nonetheless.
If you have questions, call the owners or ask somebody in Amidon.