I haven't lived in the DFW area since the early '90's so don't give to much credence to my recommendations. Jazz Alley was an excellent venue for a wide range of musical genre. There were also a number of small jazz clubs that were not so "tourist" driven.
At the time, the Deep Ellem area hosted most of the art gallaries. This link might be helpful:
http://www.10best.com/Dallas/Shoppin...ies/index.html
I hope you enjoy your visit.