1) Eat all the pork BBQ you can, it's the best on the planet. For ribs go to Central BBQ, Leonard's or Germantown Commissary. Corky's and the Rendevous are tourist traps. For chopped pork BBQ sandwiches go to the 3 places I mentioned or Tops and The BBQ Shoppe.
2) Memphis has great attractions, most notably Graceland. Yes, it's campy but worth a visit. Also visit the Pink Palace and check out what may be going on with the Wonder Series and Visit Stax Records.
http://www.memphismuseums.org For nightlife, there's no more vibrant place in the city than around Beale Street. Music, bars, crowds of people. You can go to the Gibson Guitar Factory which is close. Also check out a Memphis Redbirds minor league baseball game, the park is new and right in the city.