Baker's Ribs is the only decent BBQ in that area, otherwise everything in terms of 'cue nearby is passable.
Mama's Daughter's Diner is real close to the Anatole, real good soul food and southern comfort foods.
2014 Irving Blvd
Dallas, TX 75207-6610
The Anatole is pretty close range of good mexican places along Maple or Jefferson (in Oak Cliff). Along Maple I'd recommend Avila's while for Jefferson I suggest El Ranchito, I'm sure others will chime in with lots of good idea.
4714 Maple Ave
610 W Jefferson Blvd
A new Salvadorian restaurant, Mario Sabino's, recently opened up on Lemmon. Very good and that's also pretty closeby.
5404 Lemmon Avenue,
Bishop Arts in Oak Cliff is a short drive away, and that area has plenty of good choices with a variety of cuisines ranging from American, Mediterranean, Spanish tapas, etc., just run some searches on Bishop Arts or Bishop Arts District.
This should get you started: