In Vienna there are two ways to a civil ceremony, and both are legally equal. In the ceremony hall of one of the five registry offices (Standesamt), you marry Monday to Friday, in the morning or the afternoon. You reserve online, four weeks ahead at the earliest, and pay the federal fee of €193.
With a Dream Wedding (Traumhochzeit), the City of Vienna's term, the registry office comes to you, to a palace, a hotel, a wine tavern (Heuriger) or a rooftop terrace, on Mondays, Tuesdays, Wednesdays and Fridays at 4 and 6 p.m., and on Saturdays at 10 a.m., 12 and 2 p.m. The city charges €670 on weekdays and €995 on Saturdays, and the venue rental comes on top. You can reserve from the first working day in May for the whole following year.
Since January 1, 2019, all couples can marry in Austria. Documents, interpreters and the locations for a Dream Wedding are in my guide to Vienna's registry offices. If you are an American or British citizen, my guide Getting married in Vienna as an American or British couple lists the documents step by step.