If you are looking for indoors, here are my usual hotspots: Tuesdays and Wednesdays there is storytime at Bookpeople on Lamar. If the day is nice, it's always fun to walk over to Whole Foods, grab a coffee, and let my daughter play at the jungle gym on the terrace. Also on Wednesdays, there is a community night at the Children's Museum, which is downtown. There is a $1 entry fee, and on Sundays from 4-5 the admission is free! Another indoor activity with lots of fun families, is Sunday morning, 10:30, at Ruta Maya on South Congress. They have children's musical shows, which are free--although the musicians do accept tips. :)
Outside is where it's at, though, here in South Austin: Zilker Park, where you can ride the train and visit the water exhibit at Barton Springs; the Science and Nature Center, where they have a Dino Pit, protected trails, and a wildlife exhibit which features coyotes, owls, snakes, and lots of other critters. Don't forget about the fabulous wading pool at Deep Eddy, and the water fountain park across from Auditoreum Shores. Little Stacy park is also really nice, in Travis Heights. Finally, don't forget about the Greenbelt. My little girl loves it, and she is only 27 months old. I used to think that it would be too challenging for her, but with enough supervision and help, they really learn to get around in the outdoors! Good luck!