First, it is all dirt and dust, which is OK for people not in wheelchairs, because it is like the old west towns. But it is also uphill and it would be hard for somebody to push a wheelchair up the "Main Street."
All the stores and businesses on the Main Street have a walkway like a boardwalk in front of them, but they all have a step or two up from the dirt street, and there are no ramps at all. You could only go if you have a really lightweight wheelchair and a couple of people to lift it up. Also, there are steps from the walkway into the stores.
The train doesn't have any way for a person to get into it if they are in a wheelchair or even have any trouble walking.
What you could do, if you have somebody to push you up the Main Street, is sit behind the hitching rails and watch all the cowboy shows in the street. There is a lot of shooting though, and if you don't like that, then Wild West City is definitely not the place for you!