In a long weekend you probably won't have time to do much outside Salzburg.
In Salzburg you should go to the castle, Mozart's Geburtshaus (good to see but doesn't take long), Mirabell gardens (make sure you see the dwarves). If it's spring/summer it's a lovely walk to the castle along the Moenchsburg. It's lovely wandering around the Altstadt and you can see most of the Sound of Music locations by walking.
Hellbrunn palace with the trick fountains is a must see.
Don't bother with Mozart's Wohnhaus as it's really dull.
You should definitely eat cake at either Cafe Sacher, Cafe Bazaar or Tomaselli (or all three).
Nice places to eat are the Peterskeller, Sternbrau (for the full Austrian experience) and Zum Fidelen Affen - the restaurant opposite is also good if they are full.
DH recommends Stiegl beer I'd recommend the Marionettentheater especially if you like Mozart - we have the DVD of the Magic Flute and it's ace.
If you have time there is also the cable car, Sound of Music bus tour and day trip to Berchtesgaden. I'm not sure you will have time - of the three I'd recommend Berchtesgaden and the Eagle's Nest as the views (and bus trip) are simply breathtaking.
Mondsee is lovely and I think the church there is the one from the sound of music. There is a modern art gallery which is situated overlooking Salzburg and has a cafe with a lovely view over the city. Can't remember the name though, sorry!