Parking in Salzburg

Yes. Take a bus.

it isn't so difficult to find if you park under the mountain.

Problem is partly finding it and finding how you go once you get out of the car; but the bigger problem is the cost. It starts at 15€ and goes up from there.

As Emily says, take the bus. I always stay southwest of town on Moosstrasse where I get free parking at the hotel and a bus right in front which takes between 5 and 10 minutes to the middle of things.

Everytime I saw that parking lot under the mountain it creeped me out, but I guess it's a good use of space.

Parking at Hellbrunn is cheap and plentiful. Bus into the centre or walk by the river.

The easiest place in Salzburg to park is under the mountain. But you can also park at the train station.

We stayed in a small town about 38 miles from Salzburg for a week and we went into Salzburg twice. The first time we drove. We found parking to be very expensive so we opted to take the train the second time.

there is a major bus station/ticket office outside the mountain parking lot

I like to use P+R Salzburg Süd. The Kombiticket includes bus fare throughout the city for 5. 15 euros. The bus takes you right to the old city near the Salzach river. It's pretty stress free. You can avoid the Autobahn and the vignette cost too using secondary roads.
https://www.salzburg.info/de/reiseinfos/anreise-verkehr/auto/parken/salzburg-sued

We recently stayed here: https://stallerhof.at/en/home.html Hochreithalm Golling had really good food. Friendly and real and you can drive there too. https://www.hochreith.at/