Fuefuki, Yamanashi (笛吹市) was formed in 2004 by the merger of six smaller towns: Isawa-cho, Misaka-cho, Ichinomiya-cho, Kasugai-cho, Yatsushiro-cho and Sakaigawa-cho. Ashigawa-mura was also absorbed in 2006. Since it is a relatively new city, locals generally still refer to the areas by their town names.
Only Isawa-cho and Kasugai-cho are accessible by the Chuo Line train. Isawaonsen Station is only two stops east of Kofu on the Chuo Line, and 190 Yen. Kasugaicho Station is the 3 stops away from Kofu, and also only 190 yen. There is little of interest in the Kasugaicho Station area, and the station is so small that it is unmanned the majority of the time. (Recently there has been cause for concern that the Kasugaicho Station area is dangerous at night, especially for females traveling alone. A number of questionable activities have been reported by ALTs that use the station frequently. Exercise caution and avoid traveling alone if possible.)
Isawa-cho is the most densely populated and thus most interesting area of Fuefuki. People traveling to or through Fuefuki are most likely to stop in the Isawa area, as there's plenty of restaurants, shopping and entertainment. The main roads in Isawa are dotted with Onsen and hotels as well, making this area is very popular with Japanese tourists.
Yatsushiro-cho and Sakaigawa-cho
If you don't live in Yatsushiro-cho and Sakaigawa-cho the only reason you will likely visit is for dealings with Kotaro. Both Sakaigawa and Yatsushiro have Country Clubs with golf courses, and Yatsushiro Furosato Park has some ancient burial mounds and a fun playground with a long roller-slide and a pirate ship (If you are interested in roller-slides though, you should visit Tabayama for the longest one in Japan). The park offers a nice expansive view of the basin, and is also a great place for Hanami in the spring. There are hundreds of Sakura throughout the park, including some very large ones that are famous locally. Along with Misaka-cho and the rest of the southern basin, they are currently building the Linear Train through Yatsushiro-cho and Sakaigawa-cho, so keep an eye out for construction sites and the large dump trucks that barrel through the area.