I'm not sure this is the right forum for the question; the "South" board on the USA destination forum might be more appropriate - https://www.flyertalk.com/forum/south-454/

If you're looking to conserve flight coupons (segments) then some kind of loop tour might be the smart move. For a music emphasis loop, you might look at something like this (google the destinations) - https://goo.gl/maps/WiUqu8dY9FUFJP9S6 . It includes obvious music magnets like Memphis and Nashville, but also New Orleans (possible side trips into Zydeco country) and ends by transiting the Mississippi Delta, including stops in Rosedale and Clarksdale, at the Crossroads of the Blues. Stop at Abe's BBQ at the Crossroads and go for the full rack. Don't sell your soul.

Sun Records, Memphis



Crossroads of the Blues, Clarksdale MS





Or you don't mind a surface segment, you might want to experience beautiful Savannah and Charleston and the coastal "low country," then head north via Skyline Drive and Shenandoah National Park, as well as beautiful and historic places like Charlottesville, before ending in Washington DC. https://goo.gl/maps/dLVx69UyQ6Ea6A858

Skyline Drive in the spring



University of Virginia, Charlottesville VA (designed by Thomas Jefferson)



But these are just two of an infinity of options.