Museum Rietberg, Zürich
The Rietberg Museum is devoted to art from outside Europe. It is housed in three buildings, two of which are up on a hill called the Rietberg.
The first is the Villa Wesendonk, with collections of art from China, Tibet, Japan, India and Southeast Asia. Also there are exhibits of African art (shown here).
They are currently building a new addition to the museum, which will evidently be mainly underground so as not to impinge on the historic appearance of the villa.
A short ways down the hill is the Park-Villa Rieter, which has a lecture and concert hall, and collections of Indian, Chinese and Japanese painting and graphic art, as well as masks from the Japanese "No" theater.
(As I mentioned on the intro page, this museum has nothing to do with the composer Richard Wagner, despite the historical connections.)
This site is highly recommended to visit for several reasons. Firstly, the museum Rietberg has a first-class collection of works of art from India, Tibet, Latin America and islands in the Pacific. The exhibit is to see in three buildings: Villa Wesendonck and the (underground) linked new building where the main entrance is and which is built 12 m into the underground, and in the Parkvilla Rieter. From time to time they also have spectacular special exhibits, see website for info.
Opening hours: Wed/Thur 10 -20 h, Tue, Fri-Sun 10-17 h
Admission fee: CHF 12, CHF 16 incl. special exhibits. Free with Zürich Card
The second reason to visit is that it is an important place for history of classical music: The villa Wesendonck was built 1857 by Leonhard Zeugheer for Otto and Mathilde Wesendonck. They had met Richard Wagner in 1852 in Zürich and Otto Wesendonck graciously supported him so he could live and work in Zürich. The last years in Zürich until 1858 Wagner lived in a small timber-framed house next to the Villa. A close relationship grew between him and Mathilde Wesendonck which inspired him for his opera "Tristan und Isolde". He also set some of Mathilde's poems to music - the so called "Wesendonck songs". Wagner's wife finally provoked an eclat and Wagner had to leave Zürich for Venice where he finished "Tristan und Isolde".
The third reason is the wonderful park - it is an (almost) originally preserved English style park from the 19th century where the locals go to escape the bustle of the city. Bring a blanket and picnic, relax and - maybe - listen to some of Wagner's music from your mp3 player (I did). Or read a book, take a nap.