Japan is NOT expensive any more and hasn't been for several years. But it's our little secret and we don't want it to get out, so shhhh!!!!
What is lacking in Japan is a good tourist infrastructure. Don't expect to have everything organized for you and don't expect group tours to be a good way to go. There are few destinations in the world which reward advance planning as much as Japan. So before you go, DO YOUR HOMEWORK!
Finally, Hyatt has some excellent properties in Japan. I've only stayed at two (this one in Kyoto and, of course, the PH Tokyo) but have eaten at both the Century Hyatt and the Grand Hyatt Tokyo. I am looking forward to trying the new Hyatt in Hakone some time.
There are other Hyatts in Fukuoka and Osaka. Not that many folks get to Fukuoka, and probably not me. The Osaka Hyatt seems to be in a poor location for tourism, but why would you stay in Osaka when Kyoto is an option?
Go for it.