Of the top of my head (because I lived there) - Berlin has Tiergarten and London has Hyde Park. The latter is so so in size but the former is quite large.
Thinking further, I remembered that Paris has the Champ de Mars (surrounding the Eiffel Tower), which is about Hyde Park size.
Also plenty of cities have large forested areas that merge with the city proper and are not too far from the center, such as for example Grouse Mountain on the north side of Vancouver and Monsanto on the west side of Lisbon.
Notice how even the cities in Europe were space has been at a premium for a lot longer than in the Americas do at times have a big centrally located park.