If you want to live in Japan and the company is likely not to send you if it's too expensive, then it doesn't sound all that bad. By the time you figure in the housing, you'll be getting about 10~20% more than what you're getting now. And if the housing prices you've quoted turn out to be optimistic, you're only going to get stuck for 16% of the difference.Is this a good offer?
Keep in mind that, historically, 86 yen to the dollar is remarkably low. That puts you at risk if you have Stateside bills that you're going to be paying. If you're cutting the cord with the US dollar entirely (at least while you're here), it probably doesn't matter all that much. I had the opposite thing happen. My US salary was converted to Yen when I went "local" (at the company's request) so when the bottom dropped out of the dollar, all my Stateside expenses suddenly got cheaper. See if you can get the company to add a clause that re-adjusts your salary whenever the yen moves more than a certain percentage (I think a 10% move is a good suggested trigger). Even if you don't need it, if the dollar moves up (which it likely will eventually), you'll collect a bit of a windfall.
I assume they're paying for your moving expenses *and* for the realtor to help you find a place you like. At the prices you've quoted, it's probably not going to be huge -- but I don't know Toyohashi City so maybe things are cheap and large there. For a couple years, the experience will probably worth it. Make sure they cover furnishings, too -- and storage of your own stuff while you're here. A small aparement can become even smaller really fast if you ship over all your US-sized stuff.
I'd also get them to add a clause that says they ship you back all-expenses-paid if you're teminated for any reason other than cause. Most companies would do that anyway, but... if you get laid off but decide to stay in Japan you could use that as leverage to squeeze a bigger severance out of your former employer.
Ask them what to do about income taxes. In most cases, your Japan tax *should* end up lower than your US tax but the Japanese will count that 84% of your rent as income. And I understand that the housing exclusion has been eliminated from the US tax code. But, more importantly, you'll have to file two returns (Japan and US), and the US one will be *very* complex. Get them to assign your tax preparation to the company accountant -- not just for the two years you're here but until the effect of your stay on your tax return disappears. If you can, get them to gross-up any income you're forced to claim that is the result of the assignment (like the company-covered part of your housing).
Other than that, it's a fair offer. But if the company *needs* you, and *you* specifically, to come to Japan, it's not very generous. You'll likely be living in smaller quarters and squeezing a bit more than you do now (how much, of course, depends on your lifestyle). The days of 50~100% cost-of-living adjustments are probably over. But you could negotiate for at least 10% over your current salary (after the dollar-to-yen adjustment but not counting the housing -- in Ohio you're probably only paying 16% of what you'll be paying here for your current place, anyway ;-). It really depends on how likely they are to simply find someone else and how badly you want to go.
I hope that helps some...