Private Onsen around Tokyo

I know this might be a long shot, but I'm very interested in trying Onsen while in Japan. BUT I have quite specific conditions that I need to fulfill, mainly because I don't want to be naked in public.

1. Around Tokyo area that are covered by Tokyo Wide Pass
2. Private for 2 person
3. OR where it's allowed to wear clothing/bathing suits or even a tanktop and undies, or simply towel wrapped around the body.
4. Can be used by non staying guest, just for the day

Most people are already recommending Yunessun, but I'm not planning to go to Hakone. But it's still on the list of maybe.

Please any help is very much appreciated. I've already spent hours trying to find a place on Google, knowing that probably the reason i couldnt find any info because most of the info is in Japanese. IF you can direct me the a link, even though it's in Japanese, I can still try to use Google translate.

Thank you
- Kania -

ask those guys:
https://en.unknownjapan.net
they are "the" onsen experts and make onsen recommendations for foreigners and locals.
(they replaced their private search request now by a new forum, so you can ask there or on facebook)

I checked all private-onsens in Kanto area and this one looked the most interesting to me www.kinunoyu.com/kashikiri/
there are quite a lot of private rooms for-a-day. You need to book it by a phone (no English I think).

The onsen is around Tsukuba and can be accessed from Tokyo in 70-90 minutes (JR).

Just went there and it was nice and tidy place, 5800 yen for 2 hours on weekend. A little pricey and it's barely called onsen since there are no mountains anywhere lol