Clarksdale's best day starts with blues history and ends with live music. The Delta Blues Museum gives the town its centre of gravity, the Crossroads marker gives it its most photographed myth, and the streets around Delta Avenue carry enough record shops, murals, old buildings, and music posters to reward slow wandering.
If you have more time, look for blues trail markers around town and consider a Lower Mississippi River outing with Quapaw Canoe Company. Clarksdale is not pretty in the conventional sense, but it is unusually specific, and that is far more useful to a traveller.