Comfort Suites Austin Airport This Austin hotel is just a half mile from the Austin-Bergstrom Airport and minutes from the 6th Street city center entertainment district. It offers a free airport transfer service. Shuttle hours vary. Please contact the hotel at 512-386-6000 to get more information. Comfort Suites Austin Airport serves a hot daily breakfast and freshly brewed coffee in the lobby. The Lyndon Baines Johnson Library and Museum, the Austin Zoo, the Austin Convention Center and the Texas Capitol are all located nearby the Comfort Suites.