I don't like some of the Extended stays. You have to be careful which ones cause some have riff raff living there. The one in Pflugerville at 45 is pretty nice but stay away from the one in Round Rock, Good Luck!
Try Hawthorne suites in Austin at Mopace and 183 or Oakwood Corporate Suites at: www.Oakwood.com/Furnished
Also Try corporate furnished housing in Austin: http://www.premiercorporatehousing.com/corporateHousingResults/austin.html or