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.
Top choice: - Tokyo Station/Ginza area
For convenience 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.
There are many tourist attraction within walking distance, such as Tsukiji and the Imperial Palace.
If you need to catch a flight or take the Shinkansen early in the morning, staying in this area will save you a lot of stress as well as a taxi bill.
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...
It seems many visitors choose this area to stay. There are many big hotels in this area such as the Park Hyatt, Hilton and the Keio Plaza. There are also some budget options too, mostly in the eastern side of the station. If your visit focuses just on Tokyo, this area will be a great choice as Shinjuku is a major transportation hub.
It is within walking distance to the Meiji Shrine and exciting areas such as Harajuku or Shibuya also a quick train ride away.
However being on the western end of central Tokyo, access to Narita Airport will require more time (1.5-2hrs) as it is located NE of Tokyo. Also you need to travel across town to catch the bullet trains. A taxi to Tokyo Station will cost around 3,000 JPY.
The area called Kabukicho stays busy all night long; the excessive alcohol does result in the crime rate being higher compared with other parts of the city so if you are visiting at night use common sense and don't ask for needless trouble.
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 Prince Gallery, Hotel New Otani and The Capitol Hotel Tokyu are some of the major hotels in this area. Mainly a business zone, so on the weekends it seems to lack some energy.
Recommended more for repeat visitors to Tokyo, as the use of public transportation will be necessary to get anywhere.
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, 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 your stay in Tokyo is very quick and you are immediately continuing on to other parts of Japan, Shinagawa would be a strategic location.
You would choose this area solely for convenience as I find this area to be rather dull and lacking in any tourist attraction within walking distance.
Previously not known as an area to stay, many new hotels opened in this area just in time for the 2020 Olympics. There is no luxury hotel or any of the major American/European chains here and one should expect the rooms to be tiny even by Tokyo standards. However they are sometimes available at a reasonable price.
Most visitors will head to this area at one point during their stay in Tokyo and it can get busy during the day but after dark, the area becomes quieter and is lovely to take a walk around.
There's a direct commuter train from both Narita and Haneda airport but the downside is that the Asakusa is not directly connected with the JR system, which could be a slight inconvenience if using the bullet trains.
On the artificial 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 isolated from the rest of the city. If you want a relaxing stay, the area is great but you'll need to 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.