Daily Mandatory Charge includes: Texas Recovery Fee. In the heart of Downtown Austin, the Hilton Garden Inn Austin University Capitol District is just a few blocks away from the University of Texas and the Darrell K Royal - Texas Memorial Stadium, The Moody Center, the Capitol of Texas and a short distance to the famous 6th Street in Downtown Austin. Come enjoy a taste of Austin in our locally inspired restaurant Analog and finish your day with our one-of-a-kind view of the University, Capitol and Downtown on the 17th Floor at the Apex Rooftop.