Dominating the Serviten quarter (a small confluence of cobblestone streets lined with bars, restaurants and shops a few blocks from the Ringstrasse), the Servitenkirche was built in 1677. It was the only church outside the Innere Stadt (inner city) to survive the second Turkish siege of 1683. Its baroque interior and oval nave were inspired by the Karlskirche, but unfortunately it’s only open for Mass (see website for times); outside of this you’ll have to make do with peering through iron railings.
The adjoining monastery is an oasis of calm, in particular its inner courtyard (entry is through the door on the left).