Go to the LL homepage and click on Europe under the Destinations tab, and then click on 'See Luxury Travel Offers.' On that page, do a search based on your country of interest (Austria). It looks like there are some nice options in Vienna as well as some of the ski areas.
First of all let me say WELCOME to the Community Board. Out of curiosity, what Spas in Austria have you heard of???? As to the procedures how to search for Spas in Austria, just follow jashermd's advise to have a look on what's available on LL in Austria. As jashermd said, there are several packages at the moment. Good Luck!
Have a look at the auction page for Austria. The Hoteldorf Gruener Baum is on at a minimum starting price of $999.00 which is a steal for that price. It is a lovely spot and also has a great spa. Also note, on the auction page for the Hoteldorf Gruener Baum appears a review I have writen after we spent 5 nights there last June. Good Luck --- and let us know what you finally decided.