One, it's the site of the oldest western style department store in Japan - the Nihombashi Mitsukoshi. And two, it's known for Nihombashi Bridge, the point from which all distance is measured. Also in Nihombashi you'll find Tokyo Stock Exchange. The nearest station is Kayabacho Subway Station on the Hibiya Subway Line or the Tozai Subway Line. Leave the station via exit 10 or 11.
Trains shoot in and out with phenomenal punctuality, and frequency.
It costs only 130 yen and will allow you on the platform for up to two hours. It's also on the Marunouchi Subway Line.