Recommendations for short term accommodation in Kyoto and Osaka

Look for guesthouses and capsules hotels.
Airbnb has also some cheap offers.

Thanks for your reply Manon!
What I would like to know if any of you would recommend one in particular. Any sort of accommodation where you have been to, which is worth to visit... except capsule ehehe, not really interested to that : )

Sorry not really, it's much easier to look by yourself directly I think. Nowadays it's really easy to find cheap accomodations thanks to the internet.

I did something similar not too long ago. And I stayed at really great hostels which I would like to recommend. All three of these were extremely close to the train stations and subways,  making it easy to get out and explore:

Tokyo: Hostel East57 Asakusabashi

Kyoto: The Lower East Nine Hostel (a bit of a walk from JR Kyoto but quite a nice place)

Osaka: Iloha Hostel Namba Shinsaibashi

As others have suggested, it's also very easy to find places to stay or AirBnbs if you search further online. Good luck and have an awesome trip!