Salzburg is among the safest cities in the world, allowing you to relax and enjoy your time there. It is a small city and generally, you do not need to worry about travelling around, even late at night. However, with all cities, there are some areas that are safer than others.
The outskirts in the north of the city have a slightly higher crime rate than the test of the city. However, these are not usually areas tourists tend to flock to, so as long as you remain within the relative safety of central and southern Salzburg, you should have no concerns with safety.