To complete this list of short trips around Tokyo the destinations of Yokohama, Kamakura and Hakone should be mentioned here as well. I only passed them on my Tokaido hike so i am not able to give an in depth description but rather just give some teasers why so many people like to go to these places over the weekends.
Yokohama is a modern city in the south of Tokyo. Some of the famous attractions are Chinatown, parade of Pickachus around the end of summer and the cup noodle museum in which you can get your own cup noodle box with customized toppings.
Fun Fact: Instant noodles are originating from Japan, when the inventor was looking for an easy but durable way to preserve Ramen after the World War II. He did a long and tiresome research until he observed his wife deep frying [something] and he came up with the idea of deep frying noodles. The water would evaporate leaving tiny holes in the noodles which then get filled up again by hot water. The iconic cup actually then came when he pitched the instant noodles in America. Since they didn’t use bowls Americans used cups to prepare the instant noodles. Looking it from this perspective he then came up with the cup design which serves as bowl as well as packaging.
Kamakura is quite a touristic place and i think especially known for the Buddha statue at the Kotoku-In. Funny enough it is actually possible to go inside the Buddha. You might be disappointed by its height if you have been to Nokogiriyama seeing the 31 m tall Buddha in comparison to this 13m tall Buddha. A very popular spot is also the view of the sunset while standing on the bridge leading to Enoshima.
Hakone is located on mountain which was a very important checkpoint for travelers from and to Tokyo in the past. Today it is famous for its Hot Springs and natural beauty. If you are lucky enough you can spot Mt. Fuji from the Lake Ashinoko. If you consider to stay there for two days you might be interested into the Hakone Pass which bundles transportation into one ticket.