If you read Howard's non-Conan stories (such as his Kull stories and others) you can get a pretty good idea of what the rest of the world is like. Dale Rippke outlines it really well in his book, "Hyborian Heresies."
In a letter, Howard does mention a nameless continent in the western hemisphere, with islands adjacent to it.
In REH's "Men of Shadows," the origins of the Pictish race is outlined, showing some of the history of that nameless continent, and how the Picts (the Nameless Race) fought with the Lemurians.
In "Marchers of Valhalla," you have a story taking place toward the end of the Hyborian age. An Aesir tribe goes globe-trotting and end up at the Gulf of Mexico, looking at the Lemurian city of Khemu.
The western continent had a northern and southern portion, with a central land-bridge. The northern continent is mostly uninhabitable, although a race identifying with the Lemurians builds along the southern coast. The Lemurians on the land bridge evolve into the Toltec empire. Atlantean refugees live on the adjacent islands to the east of the landmass (Antilla). The Southern Continent becomes Mayapan. Mu lies far off the western shores of the southern continent.
