Rick Steves self-guided walking tour is very good.
Ice Cave is awesome (went today!), but if you are trying to get to Hallstatt during your time in Salzburg, too, that might be a lot to try to do.
Dinner and a Mozart concert at the fortress is great, though it may be a little warm in July (no a/c at the fortress).
Mozart Geburtshaus (Birth House) where you can stand in the room where Mozart was born. It's better than the Mozart Wohnhaus (where he lived later in life), in my opinion.
Wandering the old town.