They have great programs for kids and families, a monthly family-friendly film showing (for $5!), even theatrical summer camps! There's always something going on there, you can sign up for their email newsletter to be reminded of events.
Their Kaleidoscope Kids Series is a discounted series of fun kid friendly shows and movies. If your child takes one of the many theatre camps Julia Morgan offers, they are automatically enrolled.
The building was designed by architect Julia Morgan, who also designed Hearst Castle as well as many of the historical buildings in Berkeley. It's all redwood and used to be the St. John's Presbyterian Church, which is now located across the street.