You don't want a car in Munich. You MAY want a car in Salzburg. You CAN do almost anything by way of public transport. Where you stay depends on the car vs. public transport question.
4 days & 3 nights is a generous amount of time for Salzburg - more than you need really, for the city itself. So I assume you have some interest in the surrounding area. Will you be going to the Eagle's Nest area nearby? Have you considered visiting Halstatt (a 1-hour drive)? The various salt mines? If so, having a car would be useful, in that it allows the greatest flexibility, as well as an opportunity to just drive aimlessly for a bit in the pretty mini-Alpine scenery. It also allows you to lodge away from the town center if you wish. That's what we chose to do for our trip this summer.
If you have read the RS book already, there is little more I can tell you. There is certainly nothing wrong with staying in the town center and using the public transport options. Salzburg is geared for tourists. Keep your wallet primed and ready for action....
I know the Salzburg chapter is in both the Germany and Vienna/Austria RS books, but I think the Halstatt information is only in the Vienna/Austria book. Be sure to check that out, too.