Forests
In many cities you find urban forests with a more or less defined area. Forests are a very good starting point for areas of high biodiversity because they typically consits of very large and old trees. Especially if the forest has remained at the same place for a long time. Moreover, the forests is typically very varied as habitat.
Forests are another excellent example of a city nature type, where biodiversity would thrive if we stopped the administration. It would mean that big, old trees could fall and die, but remain in the forest to rot. Such logs is pure paradise for a lot of species, for example longhorn beetles and many wasp species.
A decrease of administration would also heighten the number of layers in the forest. A closely managed forest typically only contains of two layers: the forest floor with anemones and rocambole and the tree crowns. So if you as a species do not live either in the undergrowth or in the tree crowns, then you must find another place to stay. Several layers could be created by having fallen trees lying, let small trees and shrubs grow up, and let climbers grow up the big tree trunks. And by not cutting of the trees branches.
Of course the forests could harm humans, as we wander in there. But it is so much more fun to walk and play in a wild unmanaged forest, where you can climb the trees and the tribes and discover the animal life, instead of going for a walk in a managed beech forest, where you can only pick flowers.