They could often see it for days before they passed it and headed for the pass in the bluffs. It only took us 20 minutes to reach once we could make it out- can you imagine taking a week to travel that far?
Unfortunately, we also reached it past closing time, so we didn't go to the visitor's center and the kids didn't get Junior Ranger Badges. We were able to get close enough for some pictures, though.
Scottsbluff is the nearest city. It is large enough to have several hotels and eating establishments of various sizes, plus Walmart, etc.
Nearby attractions: Scott's Bluff Nat'l Monument, Carhenge