Foreign tourists often ask me what is really special about Tokyo. In particular when it comes to history, Kyoto has so many beautiful ancient temples, so why should I bother with history in Tokyo? The short answer is: it is Tokyo that has shaped Japan for the last 400 years! The development of Japan as we know it was orchestrated from the eastern capital since the start of the Edo period (1603-1868) when the capital was moved from Kyoto to Edo (former name of Tokyo).
One very important mechanism used in the Edo period to consolidate power in the capital was the the policy of sankin-kōtai. This policy required each major feudal lord to reside every few years in Edo for a considerable amount of time, requiring him to build a residence worthy of his status both in Edo and his own territory. His wife and kids (the heir) had to stay in Edo all the time as hostages. This put a huge financial strain on the lord, limiting his ability to wage war.
The legacy of this policy can still be seen all over Tokyo, and also outside of Tokyo as this requirement brought with it a lot of extra travel that allowed the developement of roads connecting Tokyo with the rest of Japan (the famous ones being the Tōkaidō and Nakasendō connecting Edo with Kyoto). For example, Shinjuku was the first stop on one of these routes (the Kōshū Kaidō), which connected Edo and the Kai province (nowadays Yamanashi Prefecture).
At its peak there were about 600 of these feudal lord mansions, more than there were domains as the feudal lords used to have several mansions, a small one close to Edo castle, and then bigger ones in the city or in the outskirts of the city.
There are unfortunately no fully intact feudal lord mansions in Tokyo left. If there were, they would likely be on any tourist itinerary. However, this does not mean all is lost. Two gates and two gardens have survived. Here and there are other small elements left, but they are not that impressive as the gates and gardens. Many other places have a stone marker to remember the location, but nothing can be seen anymore.
Next to these 4 places, Shinjuku Gyoen is also often seen as a remaining daimyō garden, however, the garden was completely destroyed during by air raids in 1945 and was rebuilt after the war. Higo-Hosokawa Garden is also seen as a daimyō garden.
Sankin-kōtai 参勤交代
Daimyō-yashiki 大名屋敷
At the time during the Edo period they were called Edo-yashiki (江戸屋敷) or Buke-yashiki (武家屋敷)
After the Edo period they were called Edo-hantei (江戸藩邸)