End of March short trip, where?

St Anton is a very good option but it's difficult to get cheap accommodation for a few nights.

I am assuming you would be planning on hiring a car. If so, you can reduce the cost of accommodation significantly by staying in one of the satellite villages and driving to slopes ( or use ski bus). This is perfectly feasible and does not take very long to get to slopes. For St Anton, you could look at the likes of Pettneu or Klosterle. Of course if you do this, you will miss out on legendary St Anton apres ski.