4 nights Vienna/Salzburg - need advice

Hi! We will be arriving in Vienna around noon on Dec. 17th (Thursday) and staying until Monday morning. We are lovers of architecture, history, and local taverns.

Here%26#39;s the tentative plan:

Thursday: walk around Vienna, visit Stephansdom %26amp;Christmas markets

Friday: Museum of Fine Arts, Peterskirche, %26amp; either Schoenbrunn castle or the Hofburg complex. Take late evening train to Salzburg

Saturday: Sound of Music tour, Hohensalzburg fortress, christmas market (Hellbrunn is closed this time of year?)

Sunday: early train back to Vienna. Visit one of the cemeteries, maybe National library; wander christmas markets %26amp; find wine/beer taverns.

What does everyone think? Am I right in thinking that we%26#39;re better off spending most of our time in Vienna, since this is a winter trip?

Which would you recommend for people who like architecture, furnishings %26amp; history: Schoenbrunn Castle or Hofburg?

Also, is a Sound of Music tour worthwhile in winter?

Thanks in advance for the help!