Two ways to go...I-75 to Chattanooga, I-24 to Nashville and I-40 to Memphis...or I-75 to Atlanta, I-20 to Birmingham and US78 to Memphis. It is about 240 miles from Birmingham to Memphis on US78. I've never taken this route. The route via Nashville is interstate all the way. This route does take you over Mounteagle Mountain, but it is not a hard grade. Nashville has a nice downtown area with lots of good food and music. If you stay in Nashville Two Rivers campground is about 2 miles north of Opry Land.
In Memphis checkout Tom Sawyer campground in West Memphis AR. Try for one of the river front sites. It is just a short drive into Memphis. The TN and Memphis welcome center is just across the Mississippi River (I-40)bridge. You can park for free and take the shuttle (small fare) for the several block ride into downtown. The driver gives a commentary on the historic sites that you pass. The Peabody Hotel has the famous march of ducks at 11 a.m. and 5p.m. everyday. If interested checkout the Peabody web page for more info . The Peabody is located just a few blocks from Beale St. where you will find good food and jazz. BB King has a restaurant on Beale St and the Blues City Café has great bar-b-que.
Remember its not the destination, but rather the journey.... its what's in the middle that matters the most!