Which would you chose for a 6-7 night stay?
I have been to all. My priority would be dolomites and lake como for drop dead gorgeous scenery, Bavaria for mainly castles, then Hallstatt for scenery that you can see in a day, Salzburg for a city of interest, music and lots of Mozart ref.
Salzburg is good place to base yourself. You can do day trips to Innsbruck, Munich, etc. And there's LOTS to do in the immediate area. If you want to splurge a little , stay at the Goldener Hirsch hotel. It is in Old Town and parts of it are over 400 years old. They treat you VERY well and the rooms are spacious and gracious!!! Lots of good, relatively inexpensive places to eat and Lots of great more expensive places to eat, too... Wonderful hot chocolate!!!! Good wine... Good music... Oh my, wish I was going back soon.
We have been to both areas quite extensively and have family in Baveria. We have a condo outside of Menaggio as the area is so manificently beautiful.
It is difficult to choose between the two however, the weather around Lake Como is more predictable than Baveria. It can get cold and rainy in the summer time in Baveria, yet the Southern Alps, Lake Como, has the warmth from Southern Italy. Baveria is quite open and not as congested as Como area. You can go up many mountains and ski areas in the summer time in Baveria. It is a difficult choice, but some things to consider. Either way you won't be disappointed.
Either. You can't go wrong with either.
One word of caution, you have to WANT to go to Hallstadt. It's a decent day trip from Salzburg, but there's no way to get there efficiently.