Part of 360 degree outlook from free observation floor of TMG Builing near Shinjuku station - Mt Fuji can be seen from here on a clear day.
If you arrive in Japan through Narita airport, which is a long way from downtown Tokyo, there is the private Keisei railway http://www.keisei.co.jp/keisei/tetudou/keisei_us/html/o_express.html which is much cheaper than the JR airport service, or the limousine buses which may be more convenient for your hotel, so you should think about delaying your JR pass until you are ready to do some long trips out of Tokyo. You can of course activate your pass at Narita airport for the trip into town on the luxury JR Narita express if you want, but the clock starts ticking from then. There is a fairly new deal available which may suit that doesn’t involve your JR pass - a Suica card combined with a one way trip on the luxury Narita Express. http://www.jreast.co.jp/e/suica-nex/index.html
Tourist draw cards in Tokyo include:
*Sensoji - aka the Asakusa Kannon Temple, with the Nakamise shopping arcade. Asakusa can be reached by subway, or by the Sumida river cruise (Y760)one way, which departs from Hinoide Pier, near Hamamatsucho. http://gojapan.about.com/gi/dynamic/offsite.htm?zi=1/XJ&sdn=gojapan&cdn=travel&tm=41&gps=227_156_1012_535&f=00&su=p531.31.150.ip_p531.29.420.ip_p284.8.150.ip_&tt=2&bt=0&bts=0&zu=http%3A//www.suijobus.co.jp/english/index.html
*Ueno Park - after visiting Asakusa, you could catch the Ginza subway line 3 stops to Ueno and spend some time in the Park. This is a top hanami (flower viewing) spot at cherry blossom time.
*Harajuku- reached by subway or the Yamanote loop line, this area has the famous Meiji Jingu shrine on one side of the station, and Takeshita dori on the other. This narrow lane is crowded with small fashion shops and young Japanese trendies flaunting their rather outrageous hair and clothing. It also has a Daiso store, about 4 storeys of bargains, where most stock is Y100 (plus 5%tax). Parallel to this street runs the wider Omotesando dori, with more mainstream shops, including Kiddyland and a handicraft/souvenir shop.
Some of the fashions for sale in Takeshita dori
*The free observatories above the Tokyo Metropolitan Government Building, twin towers about 10 minutes walk from the west of Shinjuku station. The walk is well signposted along arcades and tunnels, some with moving footways.
*Tokyo Tower area, Shiba Koen (park). This Eiffel tower clone is a bit expensive to enter, and the free view from the TMG building is probably better, but the park near it has a favourite temple of mine, Zojoji. In the grounds are hundreds of jizo statues for dead babies. Each stone statue, about the size of a ten pin, has a red bonnet and bib and a little holder for a colourful windmill toy. Daimon station on the Asakusa subway line, or Shibakoen on the Mita line.
*Ginza shopping district, with its designer stores and upmarket shopping, not too far from the Imperial Palace and its parks.
Daytrips from Tokyo include:
*Nikko - for Shrines and temples, and further afield, waterfalls and forests.
*Kamakura - for the outdoor Daibutsu, (Big Bronze Buddha), and lots of temples
*Mt Fuji National Park - covered later and in the section above “What to see”
Where to stay:
There are so many options - though I can recommend the Sakura Hotel in Ikebukuro. This hotel is part of a chain offering inexpensive short and long term accommodation, from dorm beds to apartments.