Cathedral, Residenzplatz and Getreidegasse with Mozart’s Birthplace, then the funicular to Hohensalzburg for the view as the lights come on.
Day 2
Gardens and music
Mirabell Gardens and the Pegasus fountain, Nonnberg Abbey, then Haus der Natur or the DomQuartier for a warm afternoon.
Day 3
Into the snow
The Untersberg cable car in the morning for snowy views over the city; Hellbrunn’s park and the zoo nearby on the way back.
Day 4
Hallstatt
Leave early by train or bus, walk the lakefront and church before the tour groups, and ride the ferry back to the station.
Day 5+
Salt or skiing
The salt mine in Hallein, or a day on the glacier at Kitzsteinhorn and the slopes above Zell am See.
Honest thought: daylight is short and many outdoor sights run winter hours. Start early, keep the evenings slow, and give Hallstatt a full day; it is not a quick hop from Salzburg.