Head out west on the Chuo line, then, take the express train from Otsuki (it's worth the few hundred yen extra - more for the leg room than the time you save!)
Going to Kawaguchiko is a funny one - Yes, you can do it in a day from Tokyo, but to be honest, at all accounts, do try and stay at least one night to enhance the feeling of pure relaxation and enjoyment once you get there. Now, I have been a few times to this area - of course, it is a popular spot for tourists and trekkers alike. Mount Fuji appears as the cute little blue & white train makes its way to the station.
However, this was the first time that I actually made an effort to explore if you like. We had a booking at a ryokan, but we also had a good few hours of time to kill. A lot of the traditional ryokans will not let you so much as set foot in their lodgings until the designated check-in time. While this does seem strict, the efforts they are going to to ensure you have a pampered and pleasant stay with them are worth it.
The tourist information centre (where great English is spoken) can help you with your bags etc. So long as you do have a booking, they can look after your bags for you and you are free to explore the surrounding area that is the lake itself!
So, for the first time, I learnt that the lake is within 5 minutes walking distance from the station and we were able to enjoy a lovely ground-level view (the last few times I have seen this lake have been from either the theme par or recently, Mount Fuji itself.)
Along the side of the lake, there are souvenir shops and lots of food places! We stopped for some awesome noodles that boiled away in front of us as we desperately showed patience secretly waiting for it to hurry up!!