The Altstadt is really quaint and has some really good shops. There are great little squares off it with cafes and market stalls selling food. The Old Town centres around one narrow street running parallel to the river Salzach. It contains good branchs of chains like Benetton as well as shops unique to Salzburg like a shop perpetually selling glass Christmas decorations.
Salzburg's cathedral in the Domplatz is also well worth a visit.

The Old Town is situated across the river from the hauptbahnhof and new town. I'm not sure what number the bus is from the Hbf, just ask at the station.

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It's Salzburg's answer to the Tower of London. There are no crown jewels but there are great views over Salzburg and there's a nice museum. It's on a crag above the Old Town and can be reached by a funicular railway near the Domplatz, or by paths (much cheaper, although steep).

The funicular station is near the Domplatz (there are signs to it). You can get a map from the Tourist Office in Mozartplatz. I don't really know where the paths begin from, but they are near the mountain's base.

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