The Ringstrasse is Vienna's great nineteenth-century statement: a broad boulevard laid over the line of the old city walls, lined with the institutions of a confident empire. Walk it westwards from the State Opera and you pass in sequence the Burggarten with its Mozart monument, the Neue Burg wing of the Hofburg closing Maria-Theresien-Platz, the twin Kunsthistorisches and Naturhistorisches museums facing each other across the square, Parliament with its Athena fountain, the neo-Gothic Rathaus and its park, the Burgtheater, the university, the Börse, and finally the Stadtpark, where a gilded Johann Strauss fiddles above the flowerbeds.
You can also ride parts of it. The old yellow sightseeing tram no longer runs, but the ordinary city trams on lines 1, 2, D and 71 each cover stretches of the Ring on a standard public-transport ticket; none completes the full circle, so you would switch lines to see everything. The sweet combination is the west half on foot - Opera to Parliament to Rathaus - and a tram for the stretch past the university and the Stadtpark when your legs have had enough.
By the time you finish at Stadtpark you are ten minutes from dinner on the Wollzeile, and the Ring at dusk, with the facades lit, is a different city altogether. Save twenty minutes for the walk back along it after dark.
Notes
Comfortable shoes are essential today; two and a half hours is comfortable at a moderate pace with photo stops. The Ring tram lines run to their own timetables, so check the departure board at whichever stop you choose rather than planning around a fixed time. A light rain jacket beats an umbrella on the exposed sections of the boulevard.