You're likely to have the museums and castles to yourself if you travel in mild October, but don't forget a raincoat. Avoid the higher altitudes, which are usually wet and sloshy rather than beautifully snow-covered.
Austria's largest film festival takes place for two weeks in mid- to late October. The screenings have a decidedly independent, fringe-like feel, which attracts a youthful audience. Parties and related events are suitably cool and urban.
From September into October, the new wines (unaged, usually light and effervescent) become available. Buy them at the local markets and vintners cellars, or attend town wine festivals in places like Budapest and Kecskemét, Hungary, and Neuchâtel and Lugano, Switzerland.