How to tag green (vegetated) areas within urban areas?

In the absence of anything better, landuse=meadow could work.

landuse=grass if covered by grass. But I prefer leisure=garden for flowered beds.

Common taggging mistakes I have seen about such things is to use landuse=greenfield ("land scheduled for new development") or landuse=village_green ("distinctive part of a village centre", quite UK specific).

I use to tag bushes as area with natural=scrub.

Here's a take on it:

• Managed publicly accessible land (not covered by other tags) is a park or garden regardless of its size (Montreal is dotted with dozens of parks often the size of a backyard).
• If an area is private land that is not built and not clearly intended to remain unbuilt, it's greenfield.
• Leftover accessible green lands are probably better dealt with by using other keys of landuse= (usually grass if it doesn't quite raise to a park level, such as a large grassy expense around some public buildings) or, less commonly, natural= (coming to mind are the spaces under high-voltage line, which are often accessible, and which I still struggle with)