Where is the city centre or downtown area of Tokyo? It is a simple question, but for a city as large as Tokyo there is no simple answer. It is important to take into account the perspective from which you ask the question.
Quick answers depending on perspective:
Historical & geographic level: Imperial Palace (former Edo Castle)
Ward level: Chiyoda, Chuo and Minato wards
Sub-metropolitan centre level: Ikebukuro, Shinjuku and Shibuya
Historical modern development level: Ginza (in Chuo ward)
A city centre or downtown is the “city’s commercial, cultural and often the historical, political and geographic heart” (source). However, a large city such as Tokyo is divided in many neighborhoods that became city centres in their own right. Historically, Edo Castle (now the Imperial Palace) is the centre of the city since the city became the centre of power early 17th century. This 115 hectares green zone stands out on a satellite image and still serves as the geographic core of the city.
Three core wards
Tokyo is mainly made up of 23 special wards and a large chunk of outlying areas in the west. The core wards are Chiyoda, Chuo and Minato. While there is no official categorization, reports from the Tokyo Metropolitan government specify these three wards as the core area (example). One of these wards has its significance right in its name: Chuo means centre. These three core wards are seeing a steady population growth right now and will see an increase of more than 30% of its current population by 2045 (source). As extension of these three core wards, another three wards are often added as “central” in the world of real estate: Shinjuku, Shibuya and Bunkyo (such as on suumo.jp).
Three sub-metropolitan centres
The Tokyo Metropolitan Government has recognized in 1958 three sub-core centres (fukutoshin in Japanese) as they have become more and more important in the city: Ikebukuro, Shinjuku and Shibuya. They coincide with major railway hubs just outside of the city centre that grew large enough to become city centres themselves. In 1982, three more sub-areas were recognized: Ueno/Asakusa (in Taito ward), Kinshicho/Kameido (in Sumida and Koto wards) and Osaki (in Shinagawa ward). Rinkai was added in 1995. I feel though that this classification leaves out many other places that are in my opinion on the same level as Osaki or Rinkai. Of the new additions I guess Ueno is the only one that truly feels as a competitor to the three initial centres that were recognized in 1958. Coincidentally, Ueno is also a major railway hub, while the others are not that significant in comparison.
Historical development of the modern city
I reckon Ginza is the true city core if you take into account how the city developed since the end of the 19th century and the functions that this part of town still fulfills today. In terms of shopping, Ginza towers over all the rest regarding variety. While it is true that you will find most shops in Shinjuku or Ikebukuro, in Ginza you will find the regular departement stores plus so much more. The flagship stores are usually located in Ginza and shops go the extra mile to please clients. When it comes to dining, the difference becomes even more significant. Most of the top restaurants in Tokyo are located in Ginza. Same goes for cafes, while Shinjuku and Shibuya host many recent cafe fads, the variety of coffee shops is remarkable limited. Ginza on the other hand has a very long cafe history and each of the trends over the last 100 years are still represented. Night life is more subdued in Ginza but many cultural venues and a large number of bars are available. Read more about Ginza in my review of the area.