Steamboat Butte is probably the best all-around hike/climb in Chadron State Park. This summit is not to be confused with the lesser-known Steamboat Butte at Fort Robinson State Park 30 miles west.
You will need a state permit to enter the park. Once there, you can pick up a state park map at the office. Park at the Sawmill Shelter and you will find the Steamboat Loop Trail near there.
The trail is a 1.8 mile loop. The quickest access to Steamboat Butte is by taking the counter-clockwise direction in the loop. That takes about 10 minutes to get to the ridge, where you will be at the south end of the "steamboat" rock formation at the end of the ridge. Look this over very carefully, as this takes good scrambling skills to make it to the main level of the top.
There is a "smokestack" rock that constitutes the true summit, but due to its soft and crumbly rock composition, it is unsafe to attempt to climb it. It is about 220 feet almost straight down on the west side to the canyon floor below. Needless to say, this is no place for any risky attempts. Chadron State
Park officials strongly discourage all attempts at scaling any of the park's buttes and rock walls. The Nebraska Interactive Trails map shows the route to the summit area by way of the Steamboat Loop Trail.