The are several options to access Kawaguchiko from Tokyo, that is other than taking one of the many popular Mount Fuji Day Trips.
Kawaguchiko By Train from Tokyo
Shinjuku Station take the JR Chuo Line (45min)
Change trains at Takao Station to the JR Chuo Honsen Line (45min)
Change at Otsuki Station take the Fuji Express (54min)
Arrive Kawaguchiko Station for viewing.
Optional – take Fujikyu Yamanashi Bus (50min) to Mt Fuji 5th Station
2390 Yen one way (JR Pass covers first two legs and Fuji Express is an extra 1,110 yen), 1500 yen for optional bus.
Kawaguchiko by Train from Hakone
Kawaguchiko by Bus from Tokyo
Shinjuku Station take the Fujikyu Bus (145min) to Mt Fuji 5th Station