As others have said, west Texas (Big Bend or the Davis Mountains) and especially the McDonald Observatory would definitely be my recommendations. However, since you mentioned you live in Dallas, I thought I would point out the
University of North Texas observatory. It was picked by D Magazine as the
best stargazing location in the area. However, I suspect most people don't know about it. It is a LOT closer than west Texas and it is free, however it is only open to the public on the first Saturday of the month.
If the skies are not cooperating or you don't want to wait until dark, you might also check out UNT's planetarium,
Sky Theater. I have not seen any of their most recent shows, but it is usually quite good. It is open to the public on Saturdays. Times and rates are on the website.