I found this site that documents where you can pull your canoe or jon boat into Lady Bird Lake. While normal motor boats are banned from use on the LBL, you are permitted to use small trolling motors. Having kayaked the lake on several occasions I can appreciate the utility in these little buggers. You can also try sailing.
If you don’t have a canoe or boat of your own, it’s easy to head down to the Texas Rowing Center (our favorite city concessionaire) and rent a canoe for the day.
Who remembers AquaFest (wiki) – Austin’s regatta? In the ’70s you could find drag boats racing on Town Lake. Before there was ACL, AquaFest was the biggest annual concert in Austin, Texas.