Mönchsberg rather unique: it is located directly behind Salzburg's historic town centre but has a countryside feel to it. It is not unusual to find cows grazing there in the summer, with their cowbells providing a musical backdrop to your stroll. Enjoy simply wondering around, or have a drink and some food at the café-restaurant at the top.
The views of Salzburg Mönchsberg offers are spectacular. You can also access the famous Hohensalzburg fortress or the Museum der Moderne, Salzburg's modern art museum. It is quite a climb though: fortunately, there is a lift in town centre to take you up.
Take the staircase down from Mönchsberg to St Peter's cemetery - definitely worth seeing.