Visit Emma Long Metropolitan Park for a leisurely hike.
http://www.ci.austin.tx.us/parks/emmalong.htm
Brushy Creek Trail in Round Rock and Cedar Park is a good place for a basic bike ride, playground areas - including a sand pit - or canooing.
http://www.wilco.org/CountyDepartments/ParksandRecreation/BrushyCreekTrail/tabid/795/language/en-US/Default.aspx
Zilker Botanical Gardens
Lady Bird Johnson Wildflower Center
Bat Watching from Congress Street Bridge
http://www.wilco.org/CountyDepartments/ParksandRecreation/BrushyCreekTrail/tabid/795/language/en-US/Default.aspx
Zilker Botanical Gardens
Lady Bird Johnson Wildflower Center
Bat Watching from Congress Street Bridge