Mt. Takamizu, is a small mountain (hill?) of 759m in the Ome area west of Tokyo. The most popular trail is to start at Ikusabata station, and then take the trail that leads up to Mt. Takamizu, after which you will pass Mt. Iwatakaeishi, and Mt. Sogaku, before coming down to Mitake.
For being a trail in the Tokyo area, it is not that crowded, and still gives a rather peaceful experience. Most local guidebooks suggests that it takes 4-6h to complete the trail, but if you are a bit used to walking, you can make it within 3h without any larger problems (it is only 10km, but of course a bit hilly).
Most signs are only in Japanese, so make sure you have printed the Kanji characters.
軍畑駅 Ikusabata station
高水山 Mt. Takamizu
岩茸石山 Mt. Iwatakaeishi
惣岳山 Mt. Sogaku
御嶽駅 Mitake station