I often hear this plan many times from people who plan to visit to Japan for sightseeing.
They usually plan to stay in Japan 1 to 2 weeks. So I tell you as a Japanese man, for your time and cost estimation.
I assume in this case, who ever is planning minimum costs, not including backpackers. It means, someone who is not rich, but they want to enjoy. Especially those in their teens and twenties.
First, It is far between Tokyo and Kyoto. Tokyo and Yokohama are near and Kyoto and Osaka are near. The distance is almost the same.
Tokyo station to Yokohama station takes about 40 minutes and the cost is about 500 Yen.
Osaka station to Kyoto station takes about 45 minutes and the cost is about 550 Yen.
100JPY(Yen) = about 1 USD = 0.7 EURO (Today’s currency exchange rate)
It takes 2 and half hours by Shinkansen(Japans fastest train) and the cost is around 10000 Yen one way.
In flight case, it takes about 60 minutes, but that’s Haneda to Osaka, so if you would go to Kyoto, you have to take busses and trains both. Total time, Osaka airport to Kyoto station, it takes about an hour.
There’s a midnight bus. The bus runs on the freeway, and it costs about 2500yen and takes about 7 hours. You can have a seat with a reservation, so you could sleep. However, if you use this, be careful of the hotel check in time and check out time, because you would have your luggage. If you would have to walk around for cant check in at your departure place and arrival place, it would be pretty tiring even though you could enjoy the view.
So, I recommend you think of your plan again if you have cost or time issues. Enjoy nice traveling.