RIDE THE BUS!
Check out CapMetro & remember, kids always ride free!
While there are some options for free parking on Saturday east of I-35, they are getting thin (try north of 7th St.); there is metered parking all over the place, and the maximum time varies. It’s free on Sunday at metered spots.
Please click link to view all parking information for the downtown Austin area: https://www.austintexas.gov/paidparking
Here’s a helpful listing/map of garages with costs.