I said this in another thread recently. The hotel reservation situation in Jpn has changed just over the past few years. Many hotels are now taking bookings up to a year in advance, even more 9 months out, probably vast majority by 6 months out, and I think only a small number of places are still making you wait until 3 months prior. The latter category is probably mostly smaller ryokans and such.

If you do a search for Shinjuku in late March on Rakuten, you will see many hotels in various categories with availabilities (APA, Keio Plaza, Hyatt Regency, etc, etc). If you back up further to late Jan, every hotel I can think of in Shinjuku shows up with available rooms.

Prices that you see many months out may actually not come down much, if at all. At least that's been my experience. And it could go up. I'm seeing 24k yen at Hyatt Regency and 19k at Century Southern Towers for next Jan. I don't think you're ever going to see rates much lower than that at those places. I booked my Noboribetsu Onsen ryokan in Jan for my July stay that I just completed. I kept checking the rates, and it just stayed the same until it started to go up around May.

So, in general, you should start looking and then book somewhere 6-9 months out. If it's peak season, like foliage in Kyoto or something, book even further out and snatch whatever is available. For ryokans and onsen places, start looking ~9 months out but then you may not be able to book the place of your choice until 3-6 months out. You can always cancel (read the cx policy, of course).