Be sure to ask somebody where "Mozart's garden" is. I don't remember its name, but it's a small garden where Mozart supposedly composed most of his "Magic Flute" piece. It's nice and... it'll give you a really nice panoramic view of Salzburg.
I only stayed for two days in Salzburg and could not visit the castle and palace that are there, but have heard that they are really nice, so if you have the time, do so!
All in all, Salzburg is a really nice city to visit, just don't be disappointed if you're looking for nightlife.
If you have any tips or comments of your own, please feel free to share them!