Dr. James Chancellor, near I-35 and Walzem. ###-###-####, Monday through Thursday. He's wonderful, and so is his staff. In the interest of full disclosure, I should tell you he's my dad, so I could be a bit biased. But I used to run his front desk, and I've seen how his patients love him-- even the apprehensive ones.
FYI, I don't think you necessarily have to take your daughter to a pediatric dentist. Children can see a general dentist, if there are no major dental problems requiring a specialist. Main consideration is how comfortable the child and her parents are with the people providing the care, so that it is a positive experience for her. (Obviously, pediatric dentists are used to dealing with children, and presumably ENJOY kids. If you find a general dentist you like, ask him/her if he's open to seeing your daughter in a couple if years.) Of course, a general dentist won't have as many toys in the waiting room and all the juvenile decor!
Dad's been in practice for over 30 years. He's not on any participating provider lists, but he'll accept assignment of benefits for most insurance plans. Nice office, but not one of those high-priced "boutique" places. He does good work.
Good luck, and welcome to San Antonio!