Briarthorn are found in level 10-25 zones and usually found near trees or near Quilboar settlements. Swifthistle may be found instead of Briarthorn due to the nature of the spawning nodes of Swifthistle. However, as of Cataclysm Expansion, The best place to farm Briarthorn would have to be Hillsbrad Foothill. Herbs in the area reappears quickly and very densely grown.
See maps below for route where to farm Briarthorn in WoW.