The Peterskirche is the showpiece Baroque church in the old city, and it is indeed impressive. It's set back a little off busy Graben and squeezed into a small square of its own, and was built by Johann Lukas von Hildebrandt in 1733. The interior is dripping with ornamentation; the heavy fresco in the dome is by Johann Michael Rottmayr, who also painted the frescoes in the Karlskirche (very much more attractively in my opinion), and there is an elaborately decorated pulpit to the left of the extravagant chancel. Opposite the pulpit is a monument by the sculptor Lorenzo Matielli, who moved to Vienna from Italy in 1712, showing the Czech martyr St John of Nepomunk being thrown off the Charles Bridge in Prague in 1393.
I visited the church briefly in the morning, dodging the tour groups, but left when Mass started at 12:30. However I noticed there would be an organ recital at 3:00, which I went back for; details in the Music Trail. I hung around afterwards to take a few more photos inside.