Zurich has a reputation for being rich, tidy and a little dull, and the first two are true. It's also one of the oldest towns in the country. The Romans ran a customs post called Turicum on the Lindenhof hill, an abbey for noblewomen was founded here in 853, and in 1519 a preacher named Huldrych Zwingli began the Swiss Reformation from the pulpit of the Grossmünster. The city joined the Swiss Confederation on 1 May 1351, and the Bahnhofstrasse, the street that made it a banking town in the popular imagination, was only laid out in 1867.
The dull part doesn't hold up. In 1916, while a war raged around neutral Switzerland, a few exiles opened a cabaret on a side street and founded Dada. About 440,000 people live in the city today, roughly a third of them foreign citizens, and the river, the lake and the hills are all a tram ride apart. What Zurich isn't is cheap, so this guide gives real numbers, from the tram ticket to the passes you probably don't need. Five days fits: the old town and the lake take two, and the Uetliberg, the art, Zurich West and the Rhine Falls fill the rest.
The days are grouped by area, so you walk more and ride less: the old town, Bahnhofstrasse and the lake, the Uetliberg and the Kunsthaus, a day trip to the Rhine Falls, and Swiss history and Zurich West. Start on a Friday. The Grossmünster tower currently opens Friday to Sunday only (check), the church is shut on Tuesdays, most museums close on Mondays and shops on Sundays, and this order fits all of that. The plan works all year, with the winter changes flagged in each day. For the country as a whole, see Switzerland.