As you travel in 2 days I would assume that you have booked already all your accommodation. So step one would be to check for each of your hotels if they have an onsen and if there is a possibility to rent a family onsen for some time. The reservation is normally done upon checkin or simply by going to the family (ie private onsen) and hope for the best.
Tokyo area: I know that there is a mixed onsen ( with bathing suits ) on Enoshima. Some parts are gender segregated others are swimsuit parts. I have never been there because it is expensive and I think the outside pools were only accessible with a swimsuit. Which I didn’t have. I actually think that the outside pools aren’t real onsen (just normal hot water) but the view seems to be breathtakingly nice.
https://enoshimaislandspa.com/enospa/facilities/Takayama area: If you have time in Takayama you could go to Hirayu onsen. It’s several onsen villages about 1,5 h by bus from Takayama. Some have mixed pools. Eg this one:
http://shinzansou.com/sp/#eng
The mixed pool here is naked for all, but in the Japanese version they also say that they have a private pool for rent. If mixed naked bathing isn’t for you, probably better to call before making the treck.
Here a list of onsen in that area that offer mixed bathing. Look out for 日帰り (it is written in a box at the end of each description and means that the place is accessible for daytripers). Then open that link and scroll down to their homepage link. It may be that some of the private onsen are only available for staying guests.
https://onsen.nifty.com/ft-konyoku/okuhidaonsenkyou-onsen/Hirayu onsen is famous. I would assume that if you ask in the tourist information in Takayama they can help.
Kyoto area: Doing a similar search for Kyoto this list comes up:
https://vokka.jp/3587It is a list of places around Kyoto where there are private onsen (貸切風呂). You’d need to look at the conditions of each. Best have your hotel call them and make the reservation for you. I think just showing up there will likely result in you not getting the private onsen. They normally have only one.
If you want to search for more possibilities try search terms as :
Name of the city (in Japanese) + 混浴 (meaning mixed bathing) + 日帰り(meaning available for day trippers) +貸切風呂 (private pool for rent).
Or just go and enjoy a normal Japanese gender separate onsen. The advantage of those is that you have much more pools available, more variety of temperatures and waters
One warning though: If you have tattoos most of the public onsen are off limits. So you would need a private bath anyway.
Have not been to any of these onsen. I have done only few mixed (public) onsen experience when traveling alone and a few with my husband when we just accidentally happened in a hotel where a private onsen was available. Here my totally personal list of favorite onsen in Japan:
http://bicycletraveljapan.blogspot.jp/search/label/Onsen+Practicalitie...Onsen is definitely one of the best experiences in Japan. Just went to one in Osaka yesterday (all segregated, which is nowadays the norm) and plan to go to an other one tonight outside of Kyoto. Bliss :-)
Enjoy your trip to Japan and your bath!
