Salzburg is known as being a sleepy town, and with a population of only 150,000, you're not going to find the variety of nightlife that you might see in the capital Vienna. That said, the city has a large student population and as such there is still an active nightlife community to be found here.
A number of bars are located near the Getreidegasse and along the Rudolfskai which runs next to the Salzbach, the river which runs through the city.
Because of the size of the inner city, most bars and clubs are within walking distance from one another so if one bar doesn't suit your tastes, it normally isn't far to the next one.
For more information about specific venues, see the Entertainment section.