Fujikyuko Railway Connection
If you want to visit Lake Kawaguchi with its views of Mount Fuji by train, you will need to transfer from JR Chuo Line to Fujikyuko Railway at Otsuki Station. The journey from Otsuki to Kawaguchiko is 26,6 kilometers, and trains stop at the closest station to Mount Fuji in Japan. A Japan Rail Pass will get you as far as Otsuki, but is not valid for travel on this railway, however you can use the new 3 day Kanto Pass.
Mount Fuji Views from Otsuki
You can also see views of Mount Fuji from Otsuki if the weather is clear. Apparently, the most symmetrical view of the mountain can be seen from here, and it was the view chosen to appear on the ￥500 note before it was replaced by a coin. Unfortunately the day I visited Otsuki, it was completely cloudy and there was no chance of seeing Mount Fuji.
The area around Otsuki is a great place for hiking. Mountain villages, hot springs and Mount Fuji views can be enjoyed along the trail, in addition to the lovely natural scenery. The Mount Iwadono trail is the closest one to Otsuki - in fact you can see the bare rock face near the peak from the station. Mount Iwadono was once the site of a castle. There is a small museum halfway up. The route on the west side of the mountain takes about an hour, and rewards the climber with stunning views.
The Monkey Bridge
If you have time, you should definitely see Saruhashi, the famous Monkey Bridge. This remarkable example of medieval Japanese engineering is one of the most famous bridges in Japan. Although the bridge is located in Otsuki City the nearest station is Saruhashi (local trains only.) However, there are no lockers there, so if you want to stow your gear before exploring, Otsuki is the place to do it.
The Katsura River that flows under Saruhashi attracts many fishermen, so I suppose it must be a good fishing area. I know you can catch much prized sweetfish there (ayu in Japanese) but I don't know what other fish there are.
Food and Drink
There are plenty of nice restaurants and cafes right outside the Station entrance, so there's no excuse for starving!