It isn't really possible to avoid I-35 in Austin, it is the main north-south thoroughfare located right in the middle of the city.
Alternatives...
Trying to avoid using I-35 would entail using Lamar blvd, a main thoroughfare with heavy urban traffic, about 100 stop lights (none of which are timed to allow free traffic flow), and dozens of Capitol Metro busses that stop in the right travel lane every block or two.
On the west side there is MOPAC (Loop 1) for a north-south thoroughfare but it is usually bumper-to-bumper stop-and-go traffic most of the day, the express lanes have tolls (which doesn't gain you much because they are also bumper-to bumper), and, like I-35, it is ALSO torn-up.
On the east side there is the 130 toll road, but it is FAR east, not anywhere close to downtown. Furthermore, they are getting ready to tear it up as well.
The environmentalists and anti-growth advocates have successfully been holding-up the expansion of Austin's road network for over 40 years. Even now they are trying to get the I-35 expansion project cancelled. Their answer is to force everyone in Austin to ride bicycles! NO KIDING!!!
