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Just over the river Arve from Jonction. Most of this woodsy bluff has been left in a more-or-less natural state, though there are walking trails around the edges. The trails connect eventually with a sidewalk which crosses a railroad bridge to the St. Jean neighborhood. There is also a small (free) zoo at the western edge of the woods. If you don't like to walk up the trail from the river you can take the bus up to Claire Vue.
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Late modern, post-modern, and contemporary works by internationally known artists, as well as a special collection of Swiss conceptual work.
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.
Worth visiting for the old Tour de L'Ile, the remains of a fortified castle erected in the 13th century.
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.