The Red Brick Road is a road that shares the spiral beginning of the Yellow Brick Road in the 1939 film, The Wizard of Oz. In the film, the road is never mentioned, though it looks like it becomes a separate road.
The road has become an internet meme, and has also been explored in various versions of Oz, including a TV series based on the concept.
In Official The Wizard of Oz merchandise
These works are officially licensed products associated with the 1939 film, so they may provide the closest to an official answer to where the road goes in that movie's continuity.
Marvelous Map of Oz
The road is the main connecting road for the Munchkin Village in Munchkinland. It goes to the Lollypop Guild's place, the Lullaby League's place, the Coroner's office, and everywhere else in the Munchkin village. (The Marvelous Map of Oz)
The road leads to the very edge of Oz where the player falls all the way down to Kansas. (LEGO Dimensions)
In Red Brick Road
A cancelled television project entitled Red Brick Road would have explored the concept behind the Red Brick Road.