I could recommend a great tailor in Austin, but not Dallas, sorry. I'm not sure if any ladies on the forum are from Dallas particularly either.
The way I found my tailor when I first moved here was to look in the paper at the local "Best Of" city awards that readers vote on. I tried a couple and then found this one, and they are great. I started slowly--had them do simple hems and things like that, before I gave them something more challenging. Things you want to look for in a good tailor would be that they listen to you, and can understand what you want, so you both are on the same page. But, you also want them to be honest with you--if an alteration will be time consuming and expensive, they should tell you. Or, if a certain thing you want done might end up making the garment fit awkwardly, they should be knowledgeable enough to let you know. I've taken some dresses and things to my tailor, and we've gotten it all pinned, and she's basically said that she likes it better the way it is, which saved me from a costly mistake.