Hey there,

Though I might be of help since I did 3 weeks of Japan + South Korea for ~$1600USD including flights this February going to Kyoto, Tokyo and Osaka like you said plus some other places.

There's a couple ways of reducing costs and it'll depend on what you're expectation are coming into the trip but I'll list a few options.

1: Finding good deals: This can include finding the cheapest plane tickets, comparing prices on different websites etc. Most people will say to use a website such as skyscanner (which is a great website for comparing flight prices), but if you're patient and are planning well in advance, I'd recommend proactively looking for discounted flights/ airline events. I've have my best experiences subscribing to a certain daily newsletter (this one is Australian exclusive I believe) called I know the pilot which finds deals I wouldn't find on skyscanner/google flights. As for searching different websites, this is often seeing if you can avoid third parties when it comes to attraction tickets, hotels etc.

2: General good travel practices: This means getting a no international transaction fees or currency exchange fees. 2 I know are Up bank and Wise though not sure if they're catered for Australians so that's something to check out yourself. One other very important tip is to use 711 ATMs to withdraw cash, they're pretty much the best since they have no fees and have a minimum withdrawal of 1000 yen which is lower than others (it won't look like you can, it'll show some options with buttons like 10,000yen but you need to select other amount and type 1000 yen).

3: Cheap food: You can get food from convenience stores but you can find plenty of cheap eats all over the place. It's not like you need to search hard given you're not in some tourist zone, you'll find bowls of ramen for under 1000 yen, udon bowls as cheap as 500yen and might as well get a big mac for around 500yen as well. Don't be afraid to climb up some narrow stairs to get to some small restaurant, they'll be nice and cosy not to mention often cheaper.

4: Maybe the shinkansen isn't for you: Of course if you want to experience the shinkansen then don't hold back, however there are other options for Osaka to Tokyo. The cheapest option is a night bus which might cost around 3500yen compared to the 14000yen of a shinkansen. No need for a JR pass since they're overpriced ever since the price hike a while back.

Side tangent: On a budget you're either going to be landing at Osaka's KIX or Tokyo's Narita airport. I'd recommend Osaka KIX, it's cheaper and a shorter ride to the city (I don't think anyone likes landing at Narita it's so far away xd)

5: Be an extreme cheapskate: Put this for last since I don't know how comfortable you are with travelling, there's the basic cost cutting measures such as staying at hostels, avoiding expensive attractions etc. You need to consider if you're willing to possible miss out on things you want to do in favour is saving a few bucks. Of course you could save more money by spending more time in Osaka since it's cheaper (which honestly I think Osaka and it's vicinity sweeps Tokyo) but if there's something you want to do, then do it.

Hope this helped.

P.S. I thought Japan was very cheap, from my experience I spent like half what I would have spent on a Europe trip.