My friend and I visited Domkirche St. Stephan a week or so ago when we were in Vienna for vacation…read moretogether.
The Cathedral is a Roman Catholic Church, the mother church of the Archdiocese of Vienna. The cathedral has some incredible architecture - Romanesque and Gothic - as it dates back to the 12th century. It seemed to be the heart of Vienna - at least as far as tourists are concerned. We must have walked past it three or more times - it's centrally located within Innere Stadt and near a lot of other Vienna attractions.
This means that Domkirche is a hot spot for tourists. It was packed - inside the cathedral, outside the cathedral, everywhere. We purchased all-inclusive tickets (25 euros each), which you have to pay for in cash. It includes a self-guided tour of the cathedral, entrance to the south and north towers, the option to join the tour of the catacombs, and more.
We enjoyed the tour of the catacombs. The guide did the tour in German and English, and it was interesting and informative. Unfortunately, the cathedral in the afternoon on a Monday was just too crowded to enjoy. We took the elevator up to one of the towers (I can't remember which), because you can only access it by elevator. The wait to go up took 10 or so minutes, because the elevator only fits a few people (maybe 4?). But the wait to get down took even longer. By then, we weren't sure we had time for the other tower (which have been the better tower anyway?).
It was interesting, and I did enjoy the catacombs tour and the views from the tower we had time for. But I recommend going as early as possible in the day to avoid the crowds so you can enjoy it.