Does "Kawaguchi" in your question refer to Lake Kawaguchiko in Yamanashi Prefecture or Kawaguchi City in Saitama Prefecture?
(When you mention the lake, please call it as Kawaguchiko, not just Kawaguchi, for disambiguation).
On the JR Nikko Line, trains are available only infrequently.
- JR-East: Timetable (in Japanese) of departures of trains on the Nikko Line from Utsunomiya Station on weekdays
http://www.jreast-timetable.jp/1703/timetable/tt0248/0248070.html: The same timetable is used also on days other than weekdays.
: The trains of the following departure time do not run to Nikko: 07:15, 07:59, 17:47 and 18:52.
Echigo-Yuzawa Station
| JR Jo(f)estu Shinkansen; about 1 hour.
Omiya Station (in Saitama Prefecture)
| JR Tohoku Shinkansen; around 25 minutes.
Utsunomiya Station
| JR Nikko Line; about 40 to 50 minutes.
Nikko Station.
Traveling from near Lake Kawaguchiko by railroad, you may need more than 4 and a half hours to get to Nikko; so it sounds better to make a Nikko trip separately from Tokyo.
Currently there is one regular JR-Tobu through Limited Express train for Tobu-nikko every day, which starts from Shinjuku Station at 07:30 and makes stops on the way at Ikebukuro, Urawa and Omiya Stations of JR plus a few Tobu stations.
If you cannot squeeze your Nikko trip into the 3-day period when your JR TOKYO Wide Pass should be valid, alternatively you can use Tobu Railway from Asakusa Station, for which case a Tobu Nikko pass (designed for foreign travelers) is worth considering.
- Japan Guide
: JR TOKYO Wide Pass
http://www.japan-guide.com/e/e2361_06.html: Tobu Nikko passes
http://www.japan-guide.com/e/e2358_002.htmlNote
: Unlike Tobu Nikko passes, a JR TOKYO Wide Pass is not usable on bus routes in Nikko City.
: A JR TOKYO Wide Pass covers a surcharge for JR-Tobu through Limited Express.
: A Tobu Nikko pass sold exclusively to foreign passengers does not fully cover a surcharge for Tobu Limited Express, but its holder is given 20 percent discount.
Enjoy your trips!
