As for specific areas w/ some small clubs and restaurants and stuff w/o all of the touristy stuff, here is a short list.
1. Deep Ellum. It has turned more into the grunge scene. Great area to go get a tattoo
2. West End. Nothing like it used to be. Some of the bars are gone. The shopping center is no more. There are some good restaurants around there but that is about it. Close to the AAC if you went to a Mavericks or Stars game.
3. McKinney Ave down close to the Crescent. Lots of little areas w/ shops and restaurants and a few small pubs/bars. One is a cigar bar that my husband and some of the guys go to on few occassions.
4. Lower Greenville. Way more to choose from if just looking in the close proximity of downtown Dallas. Check at Suede and see if they have anyone performing. If the weather is nice they have a patio up on the roof. I'd say cruise up and down Greenville to see if anything strikes you. Start at Mockingbird and go south. Campisi's is on Mockingbird between 75-Central and Greenville. Some of the best Italian food around.
5. Upper Greenville. Not like it used to be. Not as many clubs but there are a few nice spots. Nothing specifically to recommend.
6. Addison. There are places all up and down Belt Line and the Dallas North Tollway. Name it and you will find it here. Sports bars, the Improv Comedy Club, excellent steak houses, etc.
FYI!!!! Be VERY careful where you park at just about any of these locations. Only park in the lots designated for the establishment that you will be visiting. Otherwise you will get to meet the nice people at the Dallas Auto Pound that is not in a very nice area of Dallas and come out about $250+ lighter than you came.
6.