Tokyo is huge. There are thousands of stores, small shops and businesses within just a 7 mile radius. Open that radius up to include the entire city, and the number of places you can visit basically exceeds the possibility of doing this all in one lifetime (much less within a 1 week vacation trip). Which is why so few Tokyo natives have themselves visited all of the big tourist sites. (Plus, it would cost too much to check out everything.)
On top of all this is the fact that Tokyo (or Edo) has a history that dates back to well before 1457 AD, when Edo Castle was first built. This means that just about anywhere you go, there's something to visit or gawk over. One of these things is the cemetery in Sengaku-ji, 1 mile out from Roppongi (the embassy and nightlife district). Sengaku-ji (Sengaku Temple) contains the remains of the 47 Ronin, a true event that took place in Tokyo on 1701. After visiting the temple, walk around the twisty little roads that litter the backyards between the temple and the Sengaku-ji train station to get a feel for what the ronin would have been going through at the time.
The story is fully described at the wiki page, and has been turned into kabuki plays and even film. As a recap, the lord of a small domain in the countryside is called to Edo along with some of his retainers. The lord runs afoul of a corrupt court official and makes the mistake of drawing his sword against a representative of the Shogun. The lord is ordered to commit seppeku. In revenge, the retainers turn ronin (masterless samurai) and wait a full year and a half before exacting revenge against the house of the corrupt official. After that, the ronin also commit seppeku to follow their lord into the afterlife, and their ashes are then interred in Sengaku-ji.
The temple itself is nothing all that interesting, being surrounded by apartments and modern office buildings. However, the statue of the lead retainer, Ooishi Kuranosuke, is very impressive, and the cemetery itself does have an air of age and history. If you come to Japan, this is a place well worth visiting. Afterwards, there's a really nice little dessert shop half a block in front of the temple gate that serves good coffee and shaved ice if you need a snack.
(Close-up of crest on the money box in front of temple)
(Close-up of pillar detail on temple)
(Same pillar, different angle)
(Cemetery, with urn markers for some of the 47 ronin)
(Urn marker, probably for Ooishi's wife (not sure, though))