For your reference, "Tokyo Custom Tour Guides" suggests sixteen sites (twelve in and four around Tokyo). They are popular with foreign visitors or off the beaten track even for Japanese.
Each site shows its typical picture and the rough tour time from the center of Tokyo. But the destination can be modifiable according to your preference. Let's make your own private itinerary after choosing your favorite destinations, with reference to the maps of “In-Tokyo Tour” and “Around-Tokyo Tour”.
If you want more information about each place in a picture, please click it. And if you have others in mind, please let us know. We can put them into your itinerary.
Nijyubashi (Double Bridge)
Tokyo Sta. & Imperial Palace (3hrs)
Kaminarimon (Thunder Gate)
Asakusa & Ryogoku
Torii-gate of Meiji-Jingu Shrine
Meiji Shrine & Harajuku (3 hrs)
Tokyo Tower & its surroundings (3hrs)
Scramble Crossing Road
Autumn leaves in Korakuen
Korakuen Park & Kagurazaka (4hrs)
Ferry on the Edo River
Ueno Park (2hrs)
Pirate boat on Lake Ashi
Hakone & Mt. Fuji
Open-air Great Buddha
Kamakura (one day)
Time Bell Tower
Kawagoe (6 hrs)
Yomeimon Gate at Toshogu
Nikko (one day)