One of the highest buildings in the skyscraper district of Shinjuku, where you can see views of Tokyo and the area around it, including Mount Fuji (only on clear days in late winter/early spring). The plus point is that this is one of the only things you can do in Tokyo for free. The viewing area opens about 10am and closes about 10pm.
www.metro.tokyo.jp/ENGLISH/TMG/outline.htm
The nearest train station is Tocho mae.