I don't know if you've already had your trip or not, but when in Memphis you have quite a selection. You always have the famous joints like Rendesvous and Corky's. Personally, even though I've been in Memphis quite some time, I've never eaten at Rendesvous. There are those that can't stand the place and those that consider it hallowed ground.
The original Corky's on Poplar Ave. is wonderful. It is one of my favorite places to get Ribs.
I understand BB King's on Beale is supposed to have excellent ribs.
There are also some smaller places that have very loyal followings such as Interstate BBQ and Nealy's.
For BBQ that is just plain good but unpretentious you have Pig n Whistle, Brad's, and Top's. Each has two or three locations in town.