I'd have imagined in a Japanese big city nobody would visibly pay attention to a weird outfit of such modest level. While the dress code for work is strict, aren't they pretty lax with street fashion? They have those gothic lolitas, jirai kei, and whatnot strolling around.
There are definitely places like Harajuku where anything goes, but while Zanma is purposely coy on exactly where, Kogane and Goro are living somewhere on the outskirts of Tokyo which are obviously not too far from forests.
Places which would qualify are Okutama on the west, which is actually inside a national Park and has tons of outdoor stuff. Or The whole Tama (!) area in general, like the Tama hills which is suburban and tons of definite nature. Sayama Hills in Saitama, northwest of Tokyo has some nice lakes and hills ('mountains' lol) - they even call it Totoro's Forest. They seem to be somewhere between that and Real Tokyo.
Out in those relative 'boonies' (as far as a Real Shibuya Resident is concerned) it's still pretty conservative very middle class Japan and you're just not going to see gothic lolitas casually walking around. Well, it's been years since I've been to those area, but totally different vibe.