You'll probably spot Domschatz across town before you actually find this amazing place of worship. Look around inside if it's open or just take in the facade from the street.
You'll be spoiled for sightseeing choice when in Alsergrund. Domschatz is a good place to start here, but there are numerous other interesting places to enjoy. Schönbrunn Palace, Vienna State Opera, and Hofburg Imperial Palace are not far from the principal church and and will cap off your day nicely.