Overall, it's a nice hotel and I won't repeat what others have said. I'll add a few comments that may be of help if you plan to stay at the Hyatt.

Arrival
If you plan to take the Narita Express train and subway to the hotel, it's easier and quicker to get off at Tokyo Station, transfer to the Marunouchi subway line to Ginza, and transfer again to the Hibiya line to Roppongi (Exit 1C).

You may be tempted to get off the Narita Express at Shinjuku Station to transfer trains only once. However, you will have to walk considerably more once you arrive at Roppongi Station, which can be a big hassle if you have luggage. It is also a bit faster to get off at Tokyo Station.

Room with a View
One side of the hotel faces the towering Mori Tower (not a good view in my opinion). The other seems to face a rather mundane side of the city with no significant landmarks (at least I couldn't see any from my 8th floor room). If you want building across the street to block your view, you should ask for a room above the 8th floor minimum.

Swimming Pool
The swimming pool and fitness center area was visually and architecturally exciting. It was definitely worth making the time for a quick dip in the pool.

Note that the Hyatt seems to charge for everything. I forgot to bring gym shorts. The fitness center does not provide shirts and shorts like many luxury hotels do. Renting a pair of shorts was more than 700 yen (about USD 10 in 2/2012). I only had 1 hour and I wanted to swim as well, so I opted to skip the gym.

Using the locker room (with sauna and bathing facilities) was also something like USD 40. However, IT'S COMPLIMENTARY WITH A HYATT GOLD PASSPORT MEMBERSHIP. Using the full locker facilities made the fitness facilities experience much nicer. The locker room is well equipped (razors, shaving cream, juice bar, nice showers, etc.). Don't leave home without your gold passport membership (it's free)!

Beware that the use of electronic locks on lockers and the flow of using facilities (where do I shower if I want to use the pool, where do I get pool towels, etc.) is not self explanatory. Ask to be escorted as you enter the facilities.

This is a first class operation and meets the highest standards. Employees are without exception extremely professional and the rooms are immaculate. We were upgraded to a twin deluxe and the housecleaning crew come in twice a day to change towels, check on amenities and to clean the rooms. It is located next to three shopping complexes that range from casual to upper end selections and is connected by covered pathways. The hotel is also just five minutes away from Azabu Juuban by foot, which is a great residential neighborhood with great eats and ambiance. I highly recommend this hotel.

I spent a week here on business. Service and facilities were terrific. Located in the Roppongi Hills complex, there are lots of choices for restaurants. The rooms are spacious with the usual array of bathroom gadgetry and a kind of 'wet room' shower. I really enjoyed the breakfasts - not a massive selection, but a really good egg bar. Service was unobtrusive, but effective.

First of all, I also stayed the famous Park Hyatt. To be honest Hotel Park Hyatt is a better Hotel than Grand Hyatt in many ways including room quality, view, service...etc.(Do not understand me wrong Grand Hyatt quality also very very good) BUT in my next visit to Tokyo I will still stay in Grand Hyatt because it in in a very centered location and has many many good restaurants and bars around it. Thats why I review this Hotel as Excellent. In Park Hyatt you will be bored inside the Hotel but in Grand Hyatt Neverrrr. Overal it is a very good hotel. I highly recommend the Tepenyaki restaurant it is amazing. The bars are also very good.
So for couples, friends, business and solo I definitely recommend this hotel. You will not regret it. Especially If you are into nightlife then do not stay anywhere else.