Private Family Onsens.

I was reading this site here http://www.japan-guide.com/e/e3527.html about Kinosaki.

I was interested to read how some of the onsens have private family areas - 40 minutes for 3000 yen.

Could anyone tell me if there are any such onsens - nice ones - around the Osaka, Kobe, Kyoto or Wakayama areas....??

Thanks.

Yes, they can be found all across Japan. many ryokan and a few public baths have them. About onsen:
http://www.japan-guide.com/e/e2292_ryokan.html

A list of onsen with private baths in Japanese:
http://www.kashikiri-onsen.com/

If anybody can get hold of rurubu るるぶ book (it comes in magazine form) there in Japan, you can a lot of imformations and listings of onsens but it's in Japanese.
It comes in specific places like for instance, the one I have now is all about outdoor /indoor onsens, gotenburo, activities, resorts listins of HidaTakayama.
Sorry I don't have one of areas you asked.
Uji gave a good website though.