Since this is your first night you probably won't have made reservations. I'd suggest 'Pomodoro' for quick, cheap Italian food or Bobo's for Tex/Mex. They are both located in the main pedestrian area of St. Anton. Pomodoro's is on the left at the start of the pedestrian area if you're coming from the main roundabout near the main cable car station called 'Galzig'.
Bobo's is near the end of the pedestrian area on the right.
See also: http://www.maddogski.com/Austria/St+Anton/Food+and+drink