Sardine cans are very common here, and Japanese are used to them. Heads up.
Insulation is not very well used in Japan. I've heard that Kansai homes are pretty cold in winter, perhaps even worse than up here in
Hokkaido.
Fiber optic cable (hikari fiber) and cable high speed are common, but don't be surprised if your home in a rural area has slow speed. It happens.
Transportation. Figure 25,000 per month for public transportation for commuting. The rest is undefined until you actually get here.
Your explanation of "household" is amusing. I lumped those costs under grocery budget.
Yes, international school costs are a killer. Check tokyowithkids.com for tons of info. Mandatory schooling begins with kindergarten, by the way. I am surprised she doesn't know that.
Entertainment. Dinner out with Mom, Dad, and my kid runs 3000 yen at kaizen-zushi or izakaya. Figure roughly 1000 yen a head depending on where you go. Travel to a not-too-distant town, and you could be talking a couple thousand in gas, 7000-8000 per head for hotel (including breakfast), and 500-1500 yen per head for entry fees to zoos or aquariums. Lunch is what you make of it, whether 600 each for McDonalds or convenience store food. Again, your wife should know this.
As for shaken cost, I already answered that.
Health care costs? Why doesn't your wife know any of this or contact her family to ask? How much you have to pay depends entirely on what you have done. VERY ROUGHLY, I will say for most routine things, you might expect 2,000-3,000 yen coming out of your pocket. Things like ingrown toenail treatment, wart removal, flu vaccine, rash exam; add to that about 1,000-2,000 for meds. Obviously, things like MRI will be more (15,000 for one I had recently). General physical could run 5,000, I believe, but you can pay half that if the employer has it done on site.
Dry cleaning. I don't do it very much. Check here.
Cost of dry cleaning in Japan [Archive] - Japan Forums
More price info here. Your wife can easily confirm.
Prices in Japan