I've cycled from Austin to Dallas several times and from Austin to San Antonio multiple times.
My routes between Austin and Dallas generally end up following US 281. It is somewhat busy on US 67 out of DFW, but not sure where in North Texas you are coming from. After that 281 is typically reasonable as far as shoulders/traffic goes.
On the southern end, I wouldn't come via Austin, but instead take smaller routes via Blanco and Wimberley.