As much as Tokyo has to offer, just an hour on the train can reveal a whole other side of the country, and for anyone with more than three days on their schedule a day trip outside of the capital is highly recommended. Below are some ideas for day trips and excursions, although please note that some ideally require an overnight stay.
Hachijojima is one of the Izu Islands (part of Tokyo Metropolis). It is famous for its natural onsen and luscious vegetation. Possible as a day trip, but one night on the island is highly recommended. See here for more details.
A port city 40 minutes south of Tokyo that has grown over the past 150 years from a small fishing village to Japan’s second most populous city and one of its most cosmopolitan. See here for more details.