Which part of Austria?
There are a lot of cycle paths and of course plenty of moutains too, so it really depends on what you like to do. Along the Inn and Danube rivers is very nice.
There is a website here (only in German, I'm afraid) whith details of some cycle routes: http://www.radfahren.at/ It looks as though it's run by the Austrian tourist board, so you could always try phoning them for information in English.
I've cycled across Austria at the narrowest point! I think it took about half an hour.