Fewer options than Kyoto but there are still some great day trips from Tokyo.
If you like temples, then this is the place for you. Interestingly while temples in Japan often look ancient they rarely physically are, instead they are demolished and rebuilt every twenty years. Apparently a unique concept allowing them to effectively last forever, and a great way of keeping alive the skills involved in building them. Some of the most famous sights in Nikko are Rinno-ji (complex of 15 buildings), Tosho-gu Shrine (famous for it’s three wise monkeys), and Futarasan-jinja (which includes the red Sacred Bridge). The Frank Lloyd Wright designed railway station is also worth taking a closer look at .
Increasingly becoming part of the sprawling urban landscape that is Tokyo, but retaining some character of its former international past, as the main port in the area, brought to life at the Yokohama Foreign General Cemetery. The Tin Toy Museum was a random but fascinating find, and Yokohama Museum of Art is one of the best in the country, though my opinion may be biased by it offering a welcome respite from the heavy rain when I visited. Yokohama is also home to the second tallest building in Japan, the Landmark Tower, the historic ship Nippon Maur and a huge Ferris Wheel.