Your choice of accommodation can certainly influence the outcome of your vacation. I've had the experience of thinking I got a good deal on a hotel, only to discover after arriving that it was in the middle of nowhere.
Since I don't have the experience of staying at all the hotels in Tokyo, I can't say which hotels have the best service or rooms - I can give you my views on the areas though.
Our top pick: - Tokyo Station/Ginza area
By far, I will say that the area around Tokyo Station or Ginza is the best area to stay in Tokyo. It's closer to Narita Airport (while still a good hour away) and the connection for the Shinkansen is just steps away. The hotels around Tokyo Station tend to be more expensive and there is less activity in the evening. A better solution is the Ginza area, which is a short taxi ride (less than 1,000 yen) or just 1 or 2 stops on the subway, if you have mastered how to use them.
You could walk to the auctions at Tsukiji Market if you choose to get up early in the morning (note that trains in Tokyo don't run 24 hours - staying elsewhere will mean you have to take a taxi at least one-way), or watch one of the evening shows at Kabuki-Za Theatre. The shopping options are endless. The Imperial Palace isn't too far either and you could join the locals for jogging. For those on a budget, there are 1,000 yen buses operating from Narita serving Tokyo Station or Ginza directly (a third of what you pay for Narita Express trains), so you might find yourself actually saving more money, even if you have to pay extra for the rooms.
Nihombashi, Shimbashi, and Shiodome are all more or less in the same area, with the Tokyo Station a short taxi ride away. Choices range from high-end hotels such as Mandarin Oriental or the Conrad to the smaller "Business Hotels" under the APA or the Toyoko-Inn brand.
And the other areas in town...
This station is literally in the center of Tokyo and served by multiple subway lines. You will probably need to take the buses on your arrival as there are no direct train services from the airports, but once you get settled in, you'll find moving around to be very easy with use of the Metro. Shinjuku, Tokyo, Ginza, Asakusa can all be reached without changing trains. The recently opened Prince Gallery, Hotel New Otani and The Capitol Hotel Tokyu are some of the major hotels in this area. Mainly a business zone, so quieter at night and on the weekends.
Shinagawa is 20 minutes away from Haneda Airport so this is a good option if your flight is landing at HND. At the southern tip of the circular Yamanote Line, so there is a direct connection to most other major districts in Tokyo. All the Kyoto, Osaka-bound high speed Shinkansen trains stop here too, so if you are continuing on to other parts of Japan, this is going to be a convenient choice. While there is no shortage of dining options in the area, there really isn't any tourist destination within walking distance.
It seems many visitors choose this area to stay. Some of the finest hotels in Tokyo such as the Park Hyatt and the Hilton are here. It's well known for the busy nightlife and it is also a convenient base to visit the Five Lakes area of Mt. Fuji.
Note that most of the high-end hotels are on the western side of the rail station and to get to the more busier eastern end (such as Kabukicho or the Golden-Gai) you'll have to cross the tracks to the other side - this will be about a 15-20 walk.
Shinjuku is on the western end of central Tokyo, meaning it will take more time (1.5-2hrs) from Narita Airport which is NE of Tokyo. Also note you need to travel across town to catch the bullet trains. A taxi to Tokyo Station will cost around 3,000JPY.
Recently, many low-budget inns and guesthouses have opened along this area, making Asakusa (and nearby Kuramae) a popular destinations for backpackers. There are also a few hotels in the moderate price range.
Most visitors will head to this area at one point during their stay in Tokyo. Many temples, shrines, as well as the tempura and ramen places will keep you busy day and night. You could walk to the Skytree. There's a direct commuter train from both Narita and Haneda airport and also to the World Heritage site of Nikko. The only downside is that the area is not connected with the JR trains, which could be a slight inconvenience if using the bullet trains. Also there are no hotels in the "luxury" range or any of the American/European hotel brands in this area.
On the man-made island to the southeast of central Tokyo, access to both the Narita and Haneda airport is fairly easy by direct bus, and Tokyo Disneyland is nearby. Views of Tokyo Bay are wonderful at night, but the area does feel a bit detached from the rest of the city. Plan on at least 30 minutes one-way to get to central Tokyo. Also allow extra time to board the Shinkansen as there are no direct train links.
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