These three cities are very close to each other

You can choose to land at Osaka first, then travel by train to Kyoto and Nara. These three cities are cross-linked by heaps trains, buses and bullet trains.

Regarding the accomodation, type 'osaka business hotel' in google- all the hotels in the list are quite cheap, ranging from AUD %50 to 80 per night.

I will also travel to Japan from Melb in June, but will go to Tokyo and Nagoya.

Good luck