You could easily spend a week in Vienna (and 3-4 days in Prag) and not scratch the surface but 3 days in each would be a very good way of getting acquainted with these cities.
You also asked about Munich which would be a good pairing with Vienna as well.
Here are some links to recommendations:
LEADING MUNICH HOTELS
The Charles Hotel
Kempinski Vier Jahreszeiten
Mandarin Oriental
LEADING VIENNA HOTELS
Hotel Imperial
Le Méridien
WHAT TO DO
Dining in Vienna
Wining and Dining in Vienna
Activities-Sightseeing in Vienna
Vienna: Summer and Winter
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