We based in Salzburg for 6 nights last year and loved it (it was my 5th time there since I was in an exchange program during college and my husband's first).
We were there at the very end of November through the first week of December and our likes are quite similar to yours.
One day we took the bus to St. Gilgen and then ferried to St. Wolfgang. St. Gilgen is story book gorgeous at this time of year and we fell in love with it.
Another day we took the bus to Lake Koenigsee and did a boat ride then went into Berchtesgaden for lunch and strolling.
Another morning we headed to Hellbrunn and then back to Salzburg for lunch then a trip to the Fortress for the afternoon.
We visited the salt mines on another trip and spent some time in the surrounding area.
We loved our hotel, the Sheraton Salzburg, and the staff was simply wonderful. Rooms are large and modern with big king beds and big bathrooms. Of the hotels I have stayed in there, it was the best.
We discovered a small wine bar and would go there every night before having dinner at our favorite spots and we got to know the staff at the wine bar. We felt like locals and they would come and sit with us when they got off work and have a glass of wine.
We like to base ourselves in just 2-3 cities for a 12 day or so trip so we can really the area. For us, it works better than moving around a lot.
Our stay in Vienna was brief but 4 days seems good based on your plans.
We flew into Munich then headed straight for Salzburg for three nights after which we headed to Vienna. We had planned to spend three nights there as well but left after one and returned to Salzburg for three more than headed to Munich.
From Munich, we visited Linderhof Castle and drove through Fussen but did not tour the castle there.
We went to Garmisch another day and it was another fairy tale village at Christmas.
This year we headed to Berlin for 4 nights, then taking a 5 night river cruise and ending our trip in Munich. We'll day trip to Mittenwald and Regensburg from ther.
Have fun and I hope you find Austria as enchanting as we do!