Iāve already done this research before. If you want to avoid the summer heat and humidity but remain in Asia, there are only three places you can go:
Seeing how youāve already stated you want to avoid Japan and China, and flights to Mongolia are expensive, Iād say youāll need to leave Asia.
I hear Australia is pretty nice around June-August. Winter but not too cold.
Including hotels and restaurants? Those are among the things I found expensive in Okinawa, and that was Okinawaā¦
Note the āfor equivalent valueā part:
I did. At the time I went there, the equivalent value was ācheapest budget hotel I could findā and ānormal-looking restaurant with edible-looking foodā, and I found both more expensive than in Taipei. 
I mostly ended up eating from convenience stores, and I very rarely do that!
We may need to bring in our resident Ryukyu expert @urodacus to determine: are costs in Okinawa, generally speaking, higher or lower than equivalent costs in Honshu?
Guy
If Kunming qualifies, Iād say Harbin qualifies too. 
From weatherspark.com:
The hottest month of the year in Harbin is July, with an average high of 28.
The hottest month of the year in Kunming is June, with an average high of 23.
Anything over 25 (room temperature) is hot, as far as Iām concerned. You may feel differently if you grew up in Taiwan.
Okinawa is not cheap. itās one of the main destinations for Japanese tourists. most of the bigger hotels run to 400-500 USD per night. Yes, there are budget places, but there are a lot of very expensive options too (probably a higher percentage).
Foodwise, its about the same as the rest of Japan, except for fruit and veg prices which are higher. Restaurants again vary from cheap and local, to overpriced especially in the tourist areas (near the hotels) and then some very very high end stuff too.
but the beaches are free!
and weather in June is starting to get hot. Still in the high 20s, low 30s, so not too bad (relatively speaking) Only in July and August does it tip into 30-35 degrees, no variation, and often very high humidity.
the weather right now, though, is perfect.
According to Wiki, in June itās either 24.6 (1981-2010) or 25.4 (1991-2020) in Kunming with 77% relative humidity and 26.6 (1991-2020) in Harbin with 64%. Iām not sure how windy either one is.
Just sayinā.
So I guess it depends on whether you trust wiki or the weather site I quoted from.
Even then, 26/27 is hot to me (itās above room temperature). Thatās the normal daytime temperature here in Kaohsiung during early spring, which I find hot. And 24/25 is the usual evening temperature, which I find very nice.
As for the humidity, anything between 60% and 80% feels nice to me (and pretty much the same).
Thank you sir. 
Limited land plus high pressure on that limited land (from tourists and the US military, mostly) no doubt place upward pressure on costs.
When Iām in Honshu nowadays I canāt believe what good value it is, especially when compared to the frightening costs nowadays in North America.
Guy
itās the only growing prefecture in Japan. new construction everywhereā¦
while the rest of Japan is in decline, with 20% of houses vacant in the rural areas.
I wonder whatās driving the growth?
Pure speculation: I remember a while ago reading a story about state incentives to attract factory operators from Taiwan to Okinawa, where they would have (relatively) free rein to act as Taiwan factory bosses while then being able to stamp āMADE IN JAPANā on their goods.
Guy
Completely agree. Tbh as long as u avoid the usual very foreign touristy areas and choose some more āexoticā places like Gunma, northern Honshu, smaller villages in Hokkaido, JP can be cheaper.
So fly LCC to JP, maybe even better to a smaller airport (the cheapest fare up north), then JR pass (unlimited rides on JR trains, including Shinkansen) and then go up in the mountains.
Check a cheap hotel (agoda works decently in Japan, otherwise Booking works well), then eat at small joints only or have breakfast at 7-11 (which is good).
I didnāt say I wanted to avoid Japan.
Iām visiting Harbin in January for the Snow and Ice Festival.
In July 2019 I went to both Harbin and Tokyo and I was able to tolerate the weather in both.
Well, if youāre ok with Japan but want to avoid China and Mongolia, then Hokkaido would be your only option.
Oh, why didnāt you say so earlier? If youāre ok with Tokyo in the summer, and if youāre ok with Japan, then you have plenty of options.
around 25-26 degrees C of high in June sounds like Europe.
I think it can get up to about 28 or 30 in Germany in the summer, but in practice thatās really just between about 2-4pm and the temperature falls rapidly after that. You really need a coat in Germany even in the summer. Night time temperature, as in anytime after 6pm, falls rapidly to about 13C, and thatās if itās sunny. If it rains the high never exceeds about 18C.
I donāt know what Kunming is like but it sounds little different compared to Europe.
It sounds like a good destination for me if money is an issue, as going to Germany will cost me no less than 60-70k round trip, not to mention that everythingās expensive there. My only problem with China, apart from the authoritarian government, is that I really have no idea what Iād do there.
Well, no, as the thread above discusses.
Guy
Most people in this thread either gave a suggestion which the OP already disqualified in the first post, or were asking why the OP wanted to avoid getting a Chinese visa, or were having a very detailed and irrelevant discussion about Okinawa for some unknown reason. Obviously Okinawa would be too hot to visit in the summer, and therefore already disqualified.
My suggestion was the only intelligent one, but afterwards the OP said Tokyo heat is okay, which of course then opened up more possibilities.
I think I might have not been clear. I originally meant I wanted something that was below 30 degrees. Colder is better, but it looks like thereās more to do if I go to Kyoto and Osaka.