My wife is from Memphis and would kill me if I didn't recommend the Rendezvous. It's a great place and it's pretty close to Beale St. so you can eat then walk over to Beale where you'll have a world of options. It's right near the Peabody as well so you can check that out if you like.
I'd recommend the Rendezvous Special as an appetizer.
What day are you arriving, and on what side of town are you staying? Your default options for a food & music combo are Isaac Hayes and Blues City Cafe, both of which have okay food and usually pretty good music, and websites with calendars, so you can plan ahead if you want.
On weekends most every place on Beale Street's got something going, as well as a few places out east: Most of the places listed here don't have music at all, however.