You can take the Kaiji Express train directly from Shinjuku Station to Otsuki, then take the Fujikyu Line (or express train) from Otsuki to Fujisan, and finally take a bus (about 30 minutes) from there to Yamanaka. It's worth the day trip, but if you want, you can make it a few-days trip, as there are plenty of hotels, hostels and camping grounds near the lake.
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Trained journalist who's not yet jaded. Can't get enough of meeting new people, the view, cheap travel, cherry-blossom-flavored food, dinner&drinks. Painfully addicted to Japan's gochya-gochya machines. If you're the type of person to try something new vs. something you know you like, we'll get along. I'm originally from the USA. Now in Chiba Prefecture, and August 2016 marks two years in Japan. I've worked in journalism/newspapers for more than 5 years. My: Blog -- Instagram Travels in Japan (in brief): Kagoshima (Yakushima), Shizuoka (Gunma (Oze National Park, Mt. Shibutsu, Minakamix2), Tochigi (Kinugawa-Onsen, Nikko), Hyogo (Kobex2, Arima Hot Springs), Kyoto x3, Osaka, Nagano (Hakuba), Yamanashi (Katsunuma, Kawaguchiko area, Mt. Daibosatsu x3), Okinawa, Aichi (Nagoya), Kanagawa (Yokohama, Enoshima, Hakone, Kamakura), Tokyo (of course), Chiba (Choshi, Onjuku Beach, Otaki Forest, Otaki Castle, Nokogiriyama, Chiba City, Isumi, Kamogawa), Gifu, Ibaraki (Hitachi Seaside Park), Saitama (Kawaguchi), Shizuoka (Izu), Tokushima Travels outside of Japan: South Korea, Italy, Greece, France, Jamaica, Canada, Mexico x2, 22 states within the USA Future travel goals: Fukuoka, (SK) Seoul (again!), Hokkaido, Mt. Zao, Hiroshima, Mt. Fuji, Daito Islands (Okinawa), Taiwan, New Zealand, Hong Kong, Iceland, Norway, Kyrgastan