To complement your post: To be clear, no one with a deep understanding of Tokyo area considers anything outside the "23 ku's" as Tokyo. Really, Okutama, Tokyo (two hours west of world's busiest train station: Shinjuku) is comically rural -- literally, there are big mountains and small family farms that grow wasabi (delicious!). Yes, the province of Tokyo is enormous and includes lots of protected nature (and lovely hiking trails!), but when most people say "Tokyo" they mean the central 23 cities ("ku's"). If you want to get more specific, Tokyoites sometimes discriminiate between inside and outside the loop train line called Yamanote line. It is definitely the sense of urban and ex-urban in Tokyo.

And even for the "green" area, a good part of it is not that dense. I mean, it is still packed, but most of it is made of small 2 story houses rather than large apartment complexes and high rise buildings.

The real dense part that looks like the pictures of Tokyo you have most likely seen is around the Yamanote line, a train line that circles an area that is about 1/10 of the green area.

If you want to take a more principled approach to size here, you should use a metric that corresponds to how humans interact with the region. Pick a point to call the center and find all the points with a round trip time less than some number.