This is not the best part of Rock Springs, and Rock Springs is not the best part of Wyoming, but if you do end up staying in this benighted place, then you could do worse than end up at the Pour House.
They have a row of taps, but only one kind of beer coming out of them (Bud Light), and slightly more choice in bottles. With a bit of back-and-forth I was able to procure a serviceable michelada.
The place itself is kind of pretty - lots of wood on the walls, and at least one interesting piece of art involving cattle skulls. There's a front porch with very spartan benches, but it's almost superfluous because this is one of the few states where smoking is allowed indoors.
The townie regulars are working-class people and (at least on the night I was there) mostly of the loudmouth barfly type - they talk a lot but don't say anything, though I suppose they're friendly enough, and they tolerate a stranger with more grace than this particular stranger is tolerating them in this particular paragraph.
The best thing about the Pour House is that they have free wifi, and it's even pretty fast - so if you end up cooling your heels in Rock Springs, bring your laptop.