A minor summit in the section of the Northern Absarokas that spills out into Montana around Cooke City, Crown Butte is still a worthwhile objective, especially if you meet it under winter conditions as my friend Tim and I did.
Because it is pretty easy to access and routes to the top are short, Crown Butte is one of those peaks that is great for a rest day, an end-of-day quickie after having done something bigger and harder earlier, or an objective when weather appears unstable.
Views include numerous neighboring peaks, of course, but they also stretch to iconic Yellowstone Ecosystem peaks such as Pilot and Index, and they range into the remote, lightly visited backcountry of northeastern Yellowstone National Park, into the Beartooths, and into the Montana Absarokas.
Just east of Cooke City, turn onto the dirt road for Daisy Pass. You can drive to either Daisy Pass or Bull of the Woods Pass to access Crown Butte (both are about 5 miles from the pavement), and you will need high clearance for either, but you shouldn't need 4wd to get to Daisy Pass unless conditions are wet or snowy.
From either pass, pick a line and go. In normal summer conditions the approach should be really quick. As you can see in pictures here, we did not have normal conditions and had to sometimes deal with drifts of waist-deep snow. Still, the total time for the outing was only a couple of hours. Elevation gain is about 500'.
You will probably run into some 3rd class scrambling while climbing to the summit ridge, and you definitely will, with loose and exposed terrain as well, on the summit ridge.
There are some private mining claims about; try to avoid them.
Summer and early fall are best.
There is dispersed camping all over.