I did a similar trip 5 years ago pre children but we did lots of activities that kids would enjoy these are my top tips
Memphis - Civil Rights museum fantastic museum it really puts into context why America race relations is the way it is www.civilrightsmuseum.org/
Stax Museum - if you like soul music this is the history of Otis Redding, Carla Thomas and Sam & Dave. www.staxmuseum.com/
Ride a trolley bus authentic and cheap
Graceland - even if you are not a fan its a place like no other
Peabody hotel - make sure you watch the duck parade happens twice a day v cute and they spend the day splashing around in the hotel fountain. Its v expensive to stay but you can have a milkshake or cocktail and take in the atmosphere
Eat some BBQ Pork somewhere like Charles Vergo Rendezvouz
Sun Studios - Really for the music lovers as its so small but v interesting as its where Elvis cut his first record as well as Johnny Cash, Jerry Lee Lewis etc www.sunstudio.com/
Nashville - Country Music Hall of Fame
Great stops if you can fit them into itinerary
Chattanooga - Tennessee Aquarium & take a river boat ride on the Tennessee River
Huntsville - US Space & Rocket Museum- loads of massive rockets, fun day out
www.spacecamp.com/museumHome
Tupelo - birthplace of Elvis good for a short stop www.tupelo.net/
Clarksdale - home of the blues a fun place to stay if you can get a room is the shack up inn www.shackupinn.com/
You might have guessed I am a bit of a music fan. Have a great trip