Ground Zero Blues Club is the most visible live-music room in Clarksdale and the easiest place for a visitor to hear the blues without needing local contacts. It is partly theatre, partly restaurant, partly club, and deliberately rough-looking in a way that suits the town's self-image.
The room is not obscure, and that is fine. What matters is whether there is a good band on. Check the schedule, come late enough for the room to warm up, and use it as the gateway to a Clarksdale night rather than the whole story.