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Photo: Ilmari Kalkkinen, CC BY-SA 4.0 via Wikimedia Commons
Late modern, post-modern, and contemporary works by internationally known artists, as well as a special collection of Swiss conceptual work.
The Museum of Modern and Contemporary Art is the contemporary art museum of Geneva, which opened in 1994. The building is a former factory building, with 3500 m2 of exhibition space, it is the largest contemporary art museum of Switzerland.
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Four floors of stunningly beautiful watches and clocks from the last centuries, both Patek Philippe and other brands. There is also a section presenting watchmaking in practice. Bags (even shopping bags) must be kept in free lockers so don't arrive with suitcases!
See the impressive Grand Theatre (1879, renovated after a fire in 1951), the Conservatoire de musique, and the Musée Rath. Also visit the Parc des Bastions, which includes a large wall ("Mur des Réformateurs") showing some of the famous people of the Reformation movement.
This lovely tree lined park, which is home to the liberal arts campus of the University of Geneva features giant chessboards and even larger statues of Geneva's Calvinist founding fathers, and it's directly between the old town and Plain de Plainpalais, so it makes a good transitional area for exploring.
Vieille Ville
Aside of the cathedral the Old town in general is worth walking around in for an hour or two. Among the highlights are the city hall with the cannons in the little square opposite to it, Rousseau's birth house and various antique shops with all sorts of interesting stuff in the windows. A word of warning to people with physical disabilities: the Old Town, is situated on a hill with quite steep streets leading up to it.
Three floors presenting the history of Geneva from the Middle Ages until the 19th century. There's an entrance fee to the temporary exhibitions in the basement.