Being a woman that traveled and spent so much money to explore Japan, I always try to find a good deal for it. I meant, travel could be expensive but it doesn't have to go over the budget and when you're good at finding deals, you can make it!
However, a flight is not a popular option for most tourists because they usually choose over JR Pass. Since most of the route involves return trip via Shinkansen between Osaka-Kyoto-Tokyo, I do think it's the best deal out there as well. BUT, if you travel to Hokkaido, or Kyushu, or other islands, or maybe other places that will only require one-way trip and try to find a cheaper alternative than Shinkansen, blablabla, you can check flight transportation in Japan!
As long as you're a tourist visa-holder for any country, you can definitely join the hype to get a flat rate from 2 awesome flight brands in Japan, ANA and JAL
You can definitely click on both pictures and it will lead you to the link
In fact, ANA is cheaper and I have used their JAPAN FARE around 3-4 times, but I have never tried JAL. With ANA, Tokyo - Osaka is 7560 yen one way! Definitely wayyyy cheaper than one way trip via Shinkansen. Though, you have to understand that you might lose a little bit of time considering the process of check-in, immigration, boarding, airport-transfer. If time is not a matter for you and you want to save 50% of transport fee, as well as the time is right (there are some blackout dates), then I would say it's great to check it out!
I mostly use ANA to visit Hokkaido, or Kyushu. Since those two places require long travel time if it's done via Shinkansen. But once I become a student and a student-visa holder, I can no longer get an advantage of this deal (neither JR Pass) so I am a little bit disappointed :') But I have explored Japan A LOT and utilized a lot of deals before that, so I think it's okay. SOOO, while you're a tourist-holder visa, maximize your benefit!
Other cheaper alternatives to look at is to check Low-Cost-Carrier (LCC) Airlines in Japan
Below are some that you can definitely check (and it doesn't even need tourist-visa, everyone is eligible!)
My favorites are Vanilla and Peach. Vanilla Air is owned by ANA, and if you plan it right you can get even 2000 yen one way to Hokkaido from Tokyo (though through Narita, meanwhile, ANA is through Haneda). For Peach, mostly it's popular for the cheap flight overseas to Seoul, Taipei, and Shanghai. Starting around 6000 yen one way. But it's a good way to travel to Fukuoka!
So that's all the secret getting cheap japan domestic flight ticket! Hopefully, you all would be able to travel well in Japan and had fun!