So funny, S., we just moved from The Woodlands to here in November, and I like San Antonio WAY more than there! It's way more humid there, way more bugs, and way more crowded there, too.
The atmosphere here is so much more laid back and less stuffy. The Woodlands was beautiful, but I would choose San Antonio to there 100x's over. We already have great friends here, and there's more stuff to do here. We live in the NE side here, but we go downtown a lot to go to festivals, museums, etc. There, we never dared go into Houston much because it was farther, and the traffic was always AWFUL!!!
I'd say Stone Oak and 281N is pretty much most like the Woodlands, but it is so crowded, I wouldn't want to live there. I do use ABCD pediatrics up there, and LOVE them. Once you register, they'll get you in the very day you call, every time. I love it!
My cousin teaches in Alamo Heights, and it is kindof the ritzy, older-but-restored place in town. Their schools are great. I agree, I've heard NE ISD is the best, too, that's where we are.
If I could live anywhere, and didn't have to worry about a little longer commute (only 20 minutes), I would live in New Braunfuls. I love that city! Smaller, but beautiful!! And lots of fun things right there to do.
I've also heard great things about Schertz/Cibolo.
The only thing I don't like about S.A. is the lack of grocery shopping options. In Houston I had an HEB, Randalls, Kroger, Fiesta, etc. Here there's only HEB and super Walmart or Target. I miss all the good sales at the other places.
Good luck and welcome to a great, friendly, laid back place!