After fawning over the remarkable Lost in Translation, a pivotal place to visit was the New York Bar high up in the Shinjuku Park Hyatt. Since I stayed on the funkier east, walking to the business west actually took a lot longer than anticipated.
The views and the majesty are equally matched by the prices and meats are available from around the world at a premium. I seem to recall paying $60-70 for a steak from Australia (which after the fact seemed unnecessary considering I get Australian steak all over Australia usually... but you live and learn).
I don't think I need to go there again, but I'm glad I have once in my life.