There are two Neely's BBQ joints in Memphis, Neely's BBQ and Neely's Interstate BBQ.
Welcome to the website of Neely's Bar-B-Que - Memphis Style Barbeque
Interstate Barbecue | Memphis, TN
I've eaten at both multiple times and NEVER had a bad experience with either one! I know one burned down a while ago so you may want to look into that (I think it was Interstate).
Other then that you have the Rendeveuz which as mentioned is a dry rib (not cooked with sauce), I've never been there but I've heard they are good.
I ate at BB Kings once but didn't have much luck - just my opinion.
Corky's is a chain but I, and many of my friends, like their sauce. The meat can be hit or miss sometimes but the sauce is pretty good. - Corky's Ribs & Barbecue
I also had good luck at Pig on Beale St.
Which brings up Beale Street in general - you absolutely HAVE to go there when in town! I've been to Memphis quite a few times for work and only started going to Beale St. towards the end and now I wish I would've gone every time! The wife and I are thinking about heading down there for a vacation sometime in the next two or three years!
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EDIT: I've never had a BAD meal at any of these places so the only thing I can recommend is get what you like. I prefer pulled pork and ribs, when in TX though you have to buy brisket or they chase you out of the state