Yeah, I'm new to the area, too. Greentree was the best of the places I looked it, but it didn't quite suit what I was looking for and it's straight down Bandera from me, which is a super slow road at times.
What you really need is a partner! Hopefully someone a little better that nevertheless has a good time on the court with you. At any rate, drag anyone out on the courts with you that you can find. Heck, lie about your rating if you have to! Show up for the local 4.0 team and tell them you'll looking for a spot.
Seriously, good luck finding a partner if you don't have one already. It can be difficult here since there is so much emphasis on competitive play and the fact that there aren't very many public courts for people to gather and meet new folks. Most of the tennis courts in my section of NW are private and belong to home owner associations. My local courts are locked and you need a key to get on them. I couldn't tell you where a nearby public court is because I've never even seen one.
If you see some folks playing tennis in your area, just go up and say hello and ask them some questions. Being persistent is the key. Kind of tough for some people, but it's been the best way for me to find people to hit around with.
I don't know of any teachers. Sorry, can't help you there. Lot of great info on this site, though. Private teachers can be expensive, and in my limited experience it's the clubs that offer the best rates on instruction, which are frequently free for club members, though there is that pesky monthly fee thing to worry about.
Tennis is a great sport, the best I've ever played, but it's also the hardest I've ever played. Don't give up if it gets frustrating. It's clearly a life-long activity and the rewards of playing it beat any other sport I've tried.
You got any background in other sports? Probably helps to have been good at something else before taking up tennis as an adult. Man, I have seen some beginners seriously struggle on the courts next to me. Don't know how some of them stick with it. That's a where having a partner with a positive attitude helps. You two can work it out together.
What made you want to take up tennis? Know anyone who plays?
Keep us posted. I'm interested on hearing what your experiences as another new person in town are. I'll help if I can.