Austria's train network is one of Europe's best, and ÖBB runs it with Swiss-level punctuality. Fast Railjet services connect Vienna, Salzburg, Innsbruck, Graz, Linz, and Klagenfurt on frequent schedules. Many of the routes are genuinely scenic — the Semmering line south of Vienna is a UNESCO World Heritage Site, and the Arlberg route between Innsbruck and Bregenz is spectacular. If you're making more than a couple of trips, look into the ÖBB Vorteilscard: it costs around 66 euros for a year and gets you half-price tickets on most routes, which pays for itself fast.
Postbus and regional bus lines fill in where the trains don't go, especially in mountain valleys and smaller towns. In ski season, most resorts run free shuttle buses from nearby train stations. For really remote Alpine areas, you may want a car, but parking at popular trailheads can be tight in summer. Austria's roads are well maintained — just remember the motorway vignette, and budget for tunnel tolls on routes like the Brenner or Tauern.
Cable cars, gondolas, and funiculars are a regular part of getting around in the Alps, not just tourist attractions. They connect valley towns with mountain villages, hiking trails, and ski areas. Many are included in regional guest cards that your hotel provides for free. In summer, scenic mountain railways like the Schafbergbahn near Hallstatt and the Zillertalbahn in Tyrol are destinations in their own right.