Hi. Mr Silver Springer and I had a great stay at the PHT. This is an aspirational hotel--both from the service and facilities standpoint as well as the cost. We came to Tokyo as part of a MR to get AA EXP; I also had two free suite nights from the Chase CC.
I avidly read posts in this thread to prepare as well as saw the film Lost in Translation just before our trip. We had a great stay and I am very glad we came to the PHT.
Here are my tips/suggestions:
1. Everything is pretty expensive, you get more for your money if you are a Hyatt diamond and can get free breakfast, evening drinks (5-7) in the NY bar and welcome gifts. As noted above, we got two free nights in a Park Suite with a view of Mt Fuji (it was clear and we did see it yesterday) and paid for two nights and used a suite upgrade for the rest of the stay. The two nights even with a discount rate, with tax and service were about $540 each. The breakfast benefit is worth about $31 a person; diamonds get the choice of three types of breakfast American, Japanese or healthy, either room service or in the Girondole restaurant. Diamonds also get free access to the spa facilities which otherwise cost $53 a person/day; all guests can use the pool or fitness center for free. Finally for the evening drinks, 5-7 in the NY Bar, there is a diamond menu, ask for it, that has a choice of a specific type of sparkling wine, red wine, white wine or premium Asahi draft, these are service with Japanese rice crackers/nuts. The regular menu did not show the specific wines/price on the diamond menu but the Asahi beer regular cost was 1100 yen or $13. You can have a second drink if you like during that period. The view was terrific; we heard a bit of the jazz entertainment which was also nice.

2. The Concierge service is terrific, take advantage of it. The staff at the desks on the 41st floor serve as concierge and reception staff. They are terrific and can really add to the enjoyment of your stay. We especially liked the area maps they had for Shinjuku, Ginza and Harajuku areas showing recommended shops and restaurants. We also got advice on where to get money from ATM (7/11) and reservations for the airport limousine bus return to the airport.

3. Make time to go to the pool and the spa. We went to the pool twice and we were the only ones there most of the time. As reported in this thread you must wear a bathing cap which they provide but these are cloth and not uncomfortable. The pool is pleasantly warm; while I wish it was a little deeper it was a nice experience. The spa was very interesting and enjoyable. On your first entrance you are given a tour and told the rules--no shoes in spa area, no clothes in separate M/F hot tubs and saunas. There is also a relaxation room with tea, juice water and small snacks. The hot tub was very hot and relaxing; there were three different saunas, each at a different temperature. The spa had the wonderful Aesop amenities including a few types not in the room.

4. Eating options that aren't expensive: Japanese department stores have restaurants on top floors that have a very reasonable set lunch--this is your chance to try different foods. In the hotel there is a deli with sandwiches etc that is open til 7 pm. Others have written about the restaurants on the B1 level; we tried Subway on a night when we were pretty tired. One night we split a small pizza (a little larger than a dinner plate)at the NY bar; it cost $30 and was tasty and we werent very hungry.

5. For transportation to and from the hotel and Narita, try the airport limousine bus. We bought a tourist ticket that included round trip tickets and a 2 day metro pass for 6000 yen ($72) a person. The surprising thing is how far away Narita is; we arrived on a Friday night during rush hour and it took two hours to reach the hotel: the bus stops at the front door which is very nice.

6. We enjoyed an afternoon city tour from Sunrise tours that included a pick up and drop off at nearby hotels (no stop at the PHT) and at 5000 yen ($60) it was a great value and included views from the top of the World trade Center, short stop at the Palace gardens, longer stop at the Asakusa temple and shopping nearby and a 40 minute boat ride.

Overall: we had a beautiful suite, hotel staff couldnt be nicer. We really enjoyed our stay at the PHT.