The Soca / Isonzo valley in Slovenia is about an hour's drive from Klagefurt and Villach over the Predil mountain pass. Its deep limestone gorges offer a spectacular scenery and its emerald-coloured rivers are famed for some of the best kayaking and white whater rafting in Europe. Since the Soca valley is actually easier to reach from Villach and Klagenfurt than Ljubliana Slovenia's capital it's well worth a day trip if you're hanging around Carinthia for longer. Head for the town Bovec, the touristic centre of the Soca valley.
If you are in Villach take a trip to Tarvis in Italy it is about 30min by car which is a popular place to eat and shop for Carinthians.
East Tyrol, the province neighbouring Carinthia to the West, is an alpinist's paradise. The capital Lienz can be conveniently be reached by train or car.