Gotta disagree with Sam... Breadwinners is good and a nice place for the weekend "social scene" but if you want a down home breakfast (and a location IN Market Center to boot), you want Mama's Daughters' Diner.

http://www.mamasdaughtersdiner.com/breakfast1/

Wingnut you won't get much more down home Dallas than that... and those waitresses will eat your cute accent up!

As far as Tex-Mex goes, Chuys and Uncle Julios are good mainstream options where you won't go wrong. A couple more -

J. Pepe's - used to be more locations but with Dallas Tex-Mex going so "chain", the competition has been fierce. I love their stuffed fried jalepenos which in my opinion don't get much better.

http://www.jpepes.com/menu.html

I'm also very partial to El Fenix as the site of weekly childhood dinners. I don't think chips and salsa get much better than here - its low on ambiance, but high on good food for the money.

http://www.elfenix.com/

Of course, you could always post some dates in the DFW Monthly Gathering thread over in Community and perhaps some of us locals might plan something extra special for you....