Are you looking for an activity on a wet and dreary day? Wander around the interesting displays at Kaiserliche Schatzkammer. There's always an opportunity to learn a thing or two.
Situated in Innere Stadt, this museum is well worth including on your itinerary. But you'll find a great deal more to discover in this area. Schönbrunn Palace, Vienna State Opera, and Hofburg Imperial Palace aren't too far away from Kaiserliche Schatzkammer.