This is one of the most affordable and enjoyable ways to spend a day in Austin.
First, drive to the city boat dock just past Barton Springs and under the Mopac Expressway. Then, park your car and rent a canoe, kayak, or paddleboat.
If you decide to go east on the river, you can kayak straight through the downtown area and see the sights, but in my opinion, the much better direction to head is west. When you head west, you see amazing homes overlooking the lake, and you get the feeling that you're not in the city anymore and just relax.
An excellent and highly recommended way to spend the day.