Central BBQ comes highly recommended by some people. It's just across the street from the National Civil Rights Museum (Lorraine Motel where MLK was killed) if you have any interest in that sort of thing. Wife and I toured the Elvis Presley place a few years ago. It's kind of interesting, especially his restored JD 4010 with the loader. Here's a list of museums.

   https://www.tripadvisor.com/Attractions-g55197-Activities-c49-t30-Me...

Wife and I enjoyed the natural history museum, Pink Palace Museum, and the zoo. We also toured a few antebellum homes that were pretty interesting.

As others mentioned, if you leave any valuables in your car put them in the trunk or at least well hidden, lock your vehicle, be careful where you go after dark. Remember that the I-40 bridge is closed so everything is routed over the other bridge. Alternative route: cross the river at Dyersburg and come down U.S. 51 into the city. Lots of traffic lights but traffic generally keeps moving even if it is somewhat slow.