I've also recently been thirsting for a new tattoo. I went to
Downtown Tattoo last night to take advantage of their Friday the 13th special, but I missed the cut off to get on the list. I might not have the time to get one before I depart for my tour, but I'm definitely getting some new ink before Spring is over.
In addition to others' suggestions, there is also
Aart Accent, which is currently the oldest parlor in New Orleans and was founded by one the most legendary woman tattoo artists.
Best of luck with your search Dallas!