Anchorage and Austin are about 3,166 miles apart by road. Split the difference and you arrive near Portland, the city closest to the halfway point between them. That puts roughly 32 hr 17 min of driving on the Anchorage side and 35 hr 49 min on the Austin side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Portland still makes a fair, central place for Anchorage and Austin to converge, splitting the travel instead of asking one side to cross the country.
If Portland doesn't have what you're after, Seattle and Boise are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Anchorage and Austin.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.