1) Mt. Fuji
2) Kinkakuji (The Golden Pavillion in Kyoto)
3) Kiyomizudera (The Pure Water Temple in Kyoto)
4) Osaka Castle
5) Nara no Daibutsu (Giant Wooden Buddha in the city of Nara. -Biggest indoor wooden Buddha in the world).
Is the Tokyo Tower really a "famous landmark"? I think it's just a tall tower, Japan has so many other cultural things to see. Circletoe has a great list to get your started.