Gibson is a good place to check. The tour there is fantastic
Definitely spend some time just hanging out around Beale, you will be amazed at the music you will find in some places.
Definitely jump in to one of the carriage rides downtown. There isn't a better way to get a feel for that historic part of the city and get the history.
See if there are any plays / shows at the Orpheum (try ticketmaster I guess) while you are there, fantastic place to see one.
Oh head down to mud island and check out the river. When you step back and really look at it, it is quite impressive.
Sadly none of the sports have much going on right now.
Oh and my recommendation on barbeque is to try Central Barbeque, it is on Central near the East Parkway intersection, you won't be sorry.
325i 6MT, Mystic Blue, Beige w/ Poplar, Premium Package, Navi, Comfort Access, Xenons, Heated Seats, Satellite Prep (for when I want to go back and add Sirius)