Do the Blues Museum for sure. Also Ground Zero Blues Club. I if you're coming down from the Memphis area there is at least one COE campground near Tunica MS. Also casino campgrounds near Tunica.
It's been a few years, but I recall a low railroad underpass in Clarksdale.
I used to follow a website that had music venues and performers schedules, also festivals. You might do some Googling for that.
If your not used to heat and humidity you might consider spring or fall rather than summer.
Edit add....you may as well go west to Louisiana and find some classic Cajun music, since you will be nearby.