Vienna

Christine Vienna is one of my favorites- Schonbrunn Palace is a must-you should make a reservation. The Opera House-Hofburg Treasury are 2 others.
Certainly strolling around the old town and if you can make sure you attend to some music by Strauss(in the park or they do have small concerts in the centre of town).

Yes for sure the Palace.

Christine, while Salzburg is fairly close, it is about 3 hours each way by train, assuming the train is on time which was not my experience in Austria. Thus, at best, you will have a long day trip with a fairly short Salzburg visit, or you will spend more than half your 3 days in route and in Salzburg with an overnight stay.

Coffee and cake at any cafe...it doesn't have to be a famous one, they are all pretty delicious! The Leopold Museum was one of my favorites-I am a very big admirer of modern art and their collection of Schieles (one was plundered!) does not disappoint. Not only does Vienna have the best coffee in the world, it and Salzburg, in my opinion, have the absolute best beer in the world. Cold Stiegl or Zipfer on tap is a refreshing treat in the warm September sunshine.
Enjoy.

I visited Vienna in May and my #1 'must see' is Schönbrunn Palace & Gardens (no reservations needed).
If you mean to visit Salzburg from Vienna, the 3 hour train ride with 1 overnight is worth it. You can see a lot in an afternoon and the next morning, plus you get a view of the Alps almost the entire length of the train ride.