I've been to Salzburg many times in all seasons and I find that a leisurely stroll from the train station to Café 220 Grad gives you a nice tour of the essentials: riverside (especially nice in summer with market stands), Altstadt, Mozart's house, and the beautiful Dom. The Dom is really beautiful. If your stay in Salzburg is more than a layover, go up to the old castle and monastery for an awesome view over town and hit up the following:
*Café 220 Grad has some amazing quiche, chic. Chiemseegasse 5. DI - SA 9-18 Uhr.
**Zum Zirkelwirt has the best Käsespätzle I've ever had. The Spinatknödel is also out of this world. Pfeifergasse 14.
Feinkost Reichl at Wiener-Philharmoniker-Gasse 3 (or enter on Sigmund-Haffner-Gasse) is an excellent little Feinkost, Weinbar and restaurant.
Stiegl is the big, local Salzburg bier served at most bars & restaurants around town.
Kastner's Schenke is the tiny, local Salzburg bier serving small batch brews from its small hausbrauerei.
Sternbraeu is no longer small or private, but has been around in one form or another since 1542 and the famous Wolfgang hung out here.