Be warned that Mondays are dreadful days to be in Vienna with almost everything of interest to tourists being closed. Even many restaurants close on Monday. If you can arrange your trip to avoid being in Vienna on a Monday, I would advise that you do so. If you must be in Vienna on a Monday, Schoenbrun Palace should be open and you can always go to the Zentralfriedhof (Central Cemetery) to look at the graves of Bethoven, Brahms, etc. Probably two days is enough in Salzburg. Three or four might be fine in Vienna. I tend to be one of those people who doesn't see much point in spending 7+ days in a city, so keep that in mind. Sorry, can't help you with apartment rental ideas.