Austria does two things very well and they combine easily. Vienna is an imperial capital of palaces, opera and coffee houses, and Salzburg is a baroque town under a hilltop fortress. Between and beyond them, the Alps offer lakes for summer swimming and walking, and ski villages that feel like villages rather than resorts.
In summer we pair Vienna or Salzburg with the Salzkammergut lakes or the Tyrol, with trains between cities and a driver in the mountains. In winter, the Arlberg around Lech and St. Anton, and Kitzbühel in the Tyrol, are the places we send most skiers, and December brings Advent markets to every town square.
The honest caveat is popularity at particular places and times. Hallstatt fills with day visitors, so stay overnight or choose a quieter lake. Salzburg in Festival season, from late July through August, needs hotels and tickets booked early.