This plane and climbing frame are in a school in Petit-Saconnex so visit out of school hours. Nearby is probably the oldest restaurant in Geneva, fondue of course. Just past the playground is an impressive vegetable shop also.
Bois-de-la-Batie is some woodland right in the middle Geneva affectionately known as Batty Woods. The climbing frames are big, there's an Octopus, a wooden train and a paddling pool with fountain frogs. Within the woods there is an extensive animal park with goats, rabbits, wild boar, chamois, peacocks, .... On a practical note, there isn't a cafe at the park that we know of, so if you are planning to stay a while bring a bait box.
Parc de Mon Repos is the park by the lake on the way to the botanic gardens from Geneva. It looks to be good for summer with water channels and dams. There is also a recently renovated paddling pool.
As well as a strap in swing there are some springy bull-rushes, which actually look a lot better than they really are.