Start at the Lindenhof, because it is quiet in the morning and because the whole argument of the city is visible from it. The river below, the old town on both banks, the towers, and behind you a gravel terrace where men play chess and nobody hurries. Zurich rewards people who slow down in it, which is the opposite of what most visitors are told.
From there it is ten minutes downhill to the Fraumünster, and the Chagall windows are worth the detour even if you think you are finished with cathedrals. Go in the late afternoon when the west light comes through the blue.
Bahnhofstrasse runs from the lake to the station and everyone walks it. That is fine. Walk it once, then leave it. The interesting streets are the ones climbing away from it: Augustinergasse with its painted oriels, Rennweg, the small courtyards behind Münsterhof where the noise stops completely.
Lunch is a question of what kind of day you want. Kronenhalle if you want the room and the paintings and a waiter who has worked there for thirty years. Zeughauskeller if you want the opposite, which is a former arsenal, long tables and very good sausage. Both are correct. They are just different afternoons.
Then the lake. In summer the city swims, properly swims, in wooden bathing houses built out over the water. The Frauenbad dates from 1888 and becomes a bar in the evening. Visitors almost never find it, not because it is hidden but because it does not look like an attraction.
What we arrange around a day like this is unglamorous and makes all the difference. A car that is already waiting when you come out of the Fraumünster rather than one you call for. A table held at the hour you actually want it rather than the hour that was free. An appointment at a watch house where you are expected, which is a different experience from walking in.
Zurich is our home city. We are not interpreting it from a distance.
Most visitors have one day here and spend it on the wrong half of it. If you would rather not drive it yourself, the same city sits inside our private tours, and the arriving and leaving are arranged separately.