We can't really offer much in terms of setting except to say that it's vaguely Medieval, and, in this version, vaguely Scottish. You know, Braveheart-type stuff, like half-timbered cottages and wind-swept barren heaths. Based on his name, we assume that Lord Randall is a young nobleman, so personally, we imagine him coming home to a castle after a long day's hunt. He says that he's been to the "wild wood," which to us suggests a kind of Robin Hood-y setting, complete with bows and arrows, horses, and long, swishy cloaks.
Beyond that, there's really nothing else to go on. Not that it matters. If we're being honest, we'll tell you that the setting is all but irrelevant in this poem, which is part of its timeless appeal. Though it's specifically the story of a Medieval or Renaissance-era nobleman, it's also a tragic tale that we could plop down in any period and have it make sense (and hey, wasn't this story on a episode of Revenge?). Actually, part of what makes ballads and other folk songs such enduring favorites is this ability to imagine their timeless themes (like love, hate, death, et cetera) in any contemporary moment. In fact, various other folk song versions of this poem do transfer it to other times and places, depending on the singer.