If you have at least of couple of days, and want a great destination outside the cities, head for the Kiso Valley and visit the villages along the Nakasendo (the central road). This was the ancient route trod by thousands as they made their way to old Edo.
Villages along the road have been restored and life there is as it was in days of old. Stay in a traditional Japanese inn or an onsen where you can relax in the natural hot springs baths. Walk the route, or take the train between villages, or drive if you have a car available.