The Old West is one of the many realms from The LEGO Movie, and one of the few realms that are actually visited in the course of the movie. It is based heavily on the Western theme where it is home to every cowboy and Indian Minifigure.
The LEGO Movie
In the movie, Emmet finds himself in The Old West after going through a portal to get away from Bad Cop and the Robo SWAT. There, Wyldstyle figures out that he is not actually the Special. They both get on horses and go to a saloon. Vitruvius is in the saloon playing the piano. Vitruvius takes Emmett and Wyldstyle to his room, where they probe Emmett's mind.
He and Wyldstyle are both disappointed to find that Emmet displays no outside creativity, but are astonished to discover his obstacle-free mind brimming with potential creativity. With this unexpected hope, Vitruvius deems Emmet to truly be the "Special" while having his homemade birds deliver a message to the remaining Master Builders to meet at Cloud Cuckoo Land.
After this, Bad Cop tracks down Emmet and Wyldstyle in the Old West, which leads to him destroying a bridge for the train they are on. However, Batman saves them in his Batplane and reveals himself to be Wyldstyle's boyfriend, after which he flies the Batplane into the setting sun, taking them to Middle Zealand.
At the time when Wyldstyle was giving an inspirational speech for everyone to stand up to Lord Business' forces, the patrons of the saloon hear this on the phonograph. This gives them the inspiration to combine things to form devices to fight the Micro Managers.