Welcome! When my ds was that age, we liked to go to McAllister Park or Brackenridge Park. Dynamoze and Just Add Kids are fun (depending on your side of town). Lately we find ourselves at the Shops at La Cantera a lot because their playground is shaded. They also have coin operated cars in the cafeteria that my son loves (no coins needed). We have gotten involved in some Meetup.com playgroups that are good. Good luck!
I second the PP who mentioned the San Anontio Attachment Parenting group (I'm a bit partial since I'm a leader now). We have several meetings a month (will be starting another morning meeting next month) and parkdays/playdates throughout the month.
The Meetups groups (via Meetup.com) can be a good source of mommies, but you never know what you are going to get as far as vibes from a mainstream group. I love my Meetup group in Bulverde/Spring Branch (north of SA), but I think I was very lucky to find such a great group. Most of the moms are very positive discipline, breastfeed, babywear, etc.
If you can swing a zoo membership and you have little ones get it. The zoo has a younger childrens area with a shallow sandy pond they can swim in. It's so hot in SA and we used to go play in the water and then walk around the zoo while we dried so it would feel cool. Brackenridge was my fave park.