The 2 nights in CK depends on your arrival/departure time. We stayed 2 nights, but we arrived late evening and left early morning. The first night we just had dinner and walked around town. The next full day we did a walking tour, toured the castle, went to a museum, and a Church.
If you are arriving early in the morning and leaving in the late afternoon the next day it should be sufficient. It is a lovely town and was a nice rest for us to stay the 2 nights. we did doing a similar trip with with Vienna, but we had 15 nights. I wouldn't add Vienna this trip, you don't have enough time.
We stayed at the Castle View Apartments recommended by Rick and it was the best location and a nice B&B.