Wiener Linien runs five U-Bahn lines, 28 tram routes and an extensive bus network, all on one ticket, alongside the S-Bahn.
U-Bahn. U1 north–south through Stephansplatz; U2 to the MuseumsQuartier and Prater; U3 east–west through Stephansplatz; U4 to Schönbrunn and Heiligenstadt; U6 along the Gürtel. Trains every two to five minutes, and all night on Friday, Saturday and before holidays.
Trams. Lines 1 and 2 circle the Ringstrasse in opposite directions and pass most of the great Ring buildings for the price of an ordinary ticket. Tram D serves the Belvedere and the Heurigen; tram 71 the Zentralfriedhof.
Tickets. A single covers one journey with unlimited changes between modes. For a visit, buy a 24-, 48- or 72-hour pass, valid from first validation.
Validation. Stamp paper tickets once, at the start, in the blue machines. There are no barriers — the system runs on trust and plain-clothed inspectors, who fine on the spot.
Airport. Not in the core zone. The S7 is cheapest, the Railjet fastest to the Hauptbahnhof, and the CAT costs several times either to save a few minutes.
Taxis. Metered, not cheap, and generally called or taken from a rank rather than hailed. Uber and Bolt both operate.
For the detail, see Getting Around Vienna.