If you don't mind a quick drive up the beltway, I swear by Tony and Friends salon off Bellaire. While all the stylists and many of the clients are Vietnamese, I am Caucasian and have never been disappointed. I've sent 5 friends and my mother, all with varying styles and hair, and they've all loved it (my mom actually only gets her hair cut here now and she lives in Dallas!). They are inexpensive (maybe $25 or so for a shampoo, cut and style) and are worth it! Ty is my current favorite, but I also used Tony (the owner) for years. I found them 7 years ago b/c a girlfriend of mine teaches at a school nearby and all the teachers went there.
Take Beltway 8 toward Houston. exit Bellaire and go right. THey're in the first shopping center you can turn into on the left.