I don't know if it's true right now, but a few years ago when I was in Tokyo it seemed like an ideal place to stay at a really top-end hotel since the mediocre stuff was already priced so high anyway. I stayed about a week in more of a dormitory place (tiny room but did have private bath) for around 80 bucks a night, then spent my last night at the Four Seasons. It was worth every cent of the $300-odd US.

I did actually consider the Park Hyatt, but it was booked for that night. The Four Seasons is in fact the opposite sort of experience. Instead of the hustle and bustle of Shinjuku, it's tucked away in the quiet Chinzan-so Gardens. It's probably even possible to forget for a moment that you're in the middle of one of the most densely packed cities in the world. Quite a trick. Excellent service, excellent amenities. Maybe a bit much for 3-4 night stay on a trip where this could be a significant part of the cost, but if you can swing it, certainly worth it. Or consider it for one of the nights.