Veloway
Austin's best completely traffic-free road bike and inline skating path is the Veloway in far Southwest Austin at Mopac (Loop 1) and La Crosse Blvd near the Wildflower Center.
The Veloway is only open to bikes and inline skaters - no runners, walkers, dogs, joggers or other "obstacles"! It's paved, a one-way loop, and wide enough that you can comfortably pass slower bicyclists or skaters on the left.
The loop is 3.1 miles long and is not as boring as it sounds - lots of tight turns and there is one short but steep uphill.
In the spring, the wildflowers in the meadows by the Veloway are spectacular.
Many road cyclists and triathletes in Austin prefer the "Autobahn" to train on - it's an 8 mile round trip loop of State Highway 45 from the Veloway to FM 1826, where SH 45 ends with very wide shoulders, and less traffic than most Austin roads. You can certainly do both the Veloway and SH45 in a single trip.
One problem with the Veloway is that it is not bike-accessible from most of Austin because of a lack of safe bridges for bicycles over Barton Creek.