I don't know a lot about Basin at this point, other than that it's the county seat for Bighorn County, and it was founded in 1896. The population is a little over 1,000.
I've probably traveled through Basin as many times as I've been through Greybull, but while I remember Greybull, no memories come to mind about Basin.
THE MODEL RAILROAD
The track in Basin:
North is to the right in this diagram - Greybull is next along the track off to the left. To the right the track heads around to Worland, on the other side of the backdrop you can see near the bottom of the diagram (the light blue line).