Austria distills imperial grandeur and alpine splendor: Vienna's palaces, coffeehouses and concert halls; Salzburg's baroque perfection beneath castle cliffs; Innsbruck ringed by ski peaks; and lake districts — Salzkammergut, Hallstatt — that define picture-postcard Europe.
Vienna offers Schönbrunn and Hofburg palaces, the opera, Klimt at the Belvedere and café culture UNESCO lists as intangible heritage. Salzburg pairs Mozart's birthplace with Sound-of-Music scenery; the Salzkammergut's lakes include impossibly photogenic Hallstatt. Innsbruck and Tyrol anchor winter sports; the Grossglockner High Alpine Road and Wachau Valley's Danube vineyards round out the classics.
Seat of the Habsburg empire for six centuries, Austria ruled much of Europe from Vienna — a legacy visible in palaces, art collections and the world's premier concert tradition (Mozart, Beethoven, Strauss, Mahler all worked here). The empire's 1918 end and the 20th century's traumas gave way to today's neutral, prosperous republic.
A wealthy alpine economy of precision industry, tourism in both seasons (its ski regions rank with the world's best), Vienna's international organizations, and celebrated food and wine culture from schnitzel to Grüner Veltliner.
Music above all — the Vienna Philharmonic's New Year's Concert, summer's Salzburg Festival, opera for a few euros standing room — plus coffeehouse afternoons, heurigen wine taverns, ball season waltzes and pastry rivalries (Sachertorte vs. everything else).
May–September for cities, lakes and hiking; December for Christmas markets and the start of ski season, which runs into April in high Tyrol.
Vienna deserves three days minimum; Salzburg's compact center takes one or two, ideally with a Salzkammergut lakes day (Hallstatt) attached. The train between them takes about 2.5 hours.
Yes — Vienna's State Opera sells standing-room tickets for a few euros before performances, and churches and palaces host constant concerts in both cities.