While there's plenty to keep you occupied in Tokyo for days, the urge to get out and explore beyond the city limits should not be ignored. The city's a great base for numerous day trips including visits to the iconic Fuji-san (Mt. Fuji) in Fuji-Hakone-Izu National Park, one of Japan's most popular resort areas; Nikko, a popular vacation destination for Tokyo residents and the home of Tosho-gu, the astonishing shrine to the first Tokugawa shogun Ieyasu; the ancient city of Kamakura which has great historical and cultural sights; and Yokohama, a port city with an international character all its own—it's home to the country's largest Chinatown.
One caveat: the term "national park" does not quite mean what it does elsewhere in the world. In Japan, pristine grandeur is hard to come by; there are few places in this country where intrepid hikers can go to contemplate the beauty of nature for very long in solitude. If a thing's worth seeing, it's worth developing. This world view tends to fill Japan's national parks with bus caravans, ropeways, and gondolas, scenic overlooks with coin-fed telescopes, signs that tell you where you may or may not walk, fried-noodle joints and vending machines, and shacks full of kitschy souvenirs. That's true of Nikko, and it's true as well of Fuji-Hakone-Izu National Park.