When you are in the City you will see a smaller mountain to the east with a large transmitter tower on the top. This is the Gaisberg mountain and provides wonderful views of Salzburg and the surrounding mountains. There are lovely walks and in the summer you can watch the hang-gliders circling the peak before heading off into the valley below.
There is a road to the top which can be found on the 158 road from Salzburg to Wolfgangsee near to the village of Guggenthal. If you do not have access to a car then there is a bus (the 151) that leaves Mirabellplatz twice a day (currently 10:10 and 14:10) during the week that will take you to the summit. On Saturdays and Sundays there is only the 10:10. Journey time is about 35 minutes.
There are 2 cafes where you can get drinks and meals before you head back to the city. Return buses are at 11:55 and 15:55 during the week. Just the 15:55 at the weekend.