The train station is a 30 minute walk from downtown or a 5 minute cab ride. From the train station, you can see some more great European cities that are very close:
Eugendorf -- cute little Salzburg suburb, one stop away on the commuter train
Vienna -- 3.5 hours away
Prague -- 6 hours away
Venice -- circa 6 hours away
Munich -- 1 hour away
Zurich -- circa 4 hours away
I'd highly recommend Prague.
Here's the map of that EC Train that I took from Vienna to Salzburg.
The name of the train is 569 Vorarlberg.
It passes, even stops at : Vienna (Wien)
From Bregenz, the same train would depart back to Vienna.
From Munich there are several trains to get to Salzburg. In the way you see lots of nice lanscapes and villages. Here you can check timetables and prices (http://www.bahn.de ).
If you want to check it from the web of Austria: http://www.oebb.at
To visit Salburg do it walking. From the station you can go walking to the interesting area, it's not a long trip.
When arriving in Salzburg by train - have a look on the right side ( when coming from Germany )
The train will pass slowly the bridge over the river Salzach and you will have a great first view of the City and the castle "Hohensalzburg" from the train.
The trainstation is just a few steps from Mirabellgarten & Schloß Mirabell ( 5 minutes to walk )
We took a train from Vienna to Salzburg using our Eurail pass. It took about three hours to get there.
Then we took a train from Salzburg to Munich (also with our Eurail pass) which took almost two hours.
If you want travelling around Salzburg by Train, the ÖBB have his own homepage www.oebb.at, you can book tickets online and see special offerts.
If you would travel from Salzburg to Vienna and you are not a student, buy the "half-price-pass" / "halbpreis-ticket" (or "vorteilscard") directly on the train-desk (you pay a certain amount for this card and get all trains for the half price - it is also cheaper if you travell only once!)
many trains from everywhere , the main line is paris-strasbourg-münchen-salzburg-wien ; but there is also a line to bregenz(vorarlberg) and to venezia(italia)
The best way in and out was by train, it drops you off within walking distance of many hotels and a long walk to Old Town.