Late March is a great time to visit Austin. You can typically expect pleasant spring weather with temperatures in the 70s-80s during the day. However, Texas weather can be unpredictable—some years it's warm and sunny, while other times you might encounter rain or cooler evenings.
We recommend packing layers, including a light jacket or sweater, and bringing an umbrella or rain jacket just in case. Oh, and don't forget comfortable walking shoes!