You can tour the Stax studios as well as Sun. Both are "historic" ~ no longer in commercial use ~ but well-developed as museum sites. When I visited (about 6 years ago), They were in the process of building an addition to the Stax complex.

Pretty much any barbeque joint in the area is bound to be pretty good; I'm sure that locals and "insiders" could debate all day about which is better than another. We ate at one of two restaurants run by Interstate BBQ, just off the I-55 near the southern edge of the downtown area. No complaints!

Did any mention Graceland? I've never been, but for many folks, that's the single most important pilgrimage you can make when in Memphis...