--Asakusa
--Meiji Shrine (Jingu)
--Shibuya
--Harajuku Takeshita-dori
--Roppongi (night life)
--Yoyogi Park on weekend morning
-- Jiyugaoke
-- Kamakura (a good day-trip from Tokyo)
# You can get off at Harajuku station, then have a walking tour through Meiji Shrine ---> Omote-sando--> then arrive in Shibuya area (the station). Or you can do it vice verse.
# Yoyogi Park is fun to visit on weekends. And it`s very close to Meiji Shrine. (the Harajuku station)
# If you like shopping for home accessories, or little cute, chic, designed things... for your home, you need to go Jiyugaoke. It`s a very chic area has a lot cute stores!
# If you have time, take JR to visit Kamakura. It takes about one hour from Tokyo station. It is definitely worthy to visit if you have time. There are more than 10 well-preserved ancient Temples and Shrines. It`s very classic!