A quick survey of the locals (including a pair who specialise in car repairs due to damage caused by frequent hail in these parts, yes really) uncovered 2 Doors Down, a dedicated burger diner/restaurant a short walk from my motel in the centre of Cheyenne, Wyoming. Their vibe is cool, fresh and genuine and they set out their stall early with a claim to have been "Flippin' great burgers since 2009".
Just like Gourmet Burger Kitchen back in the UK, you order from a blackboard menu at the front, take a number flag and from then on it's table service all the way. There's a few key differences though, the standard drinks fountain (soft drinks, coke, lemonade etc) is bottomless but, potato lovers, so are the fries. Whenever a member of staff wanders by they latch onto an empty looking vessel, spirit it away and return with more of the same. It's a gimmick, but a great one.