I am copying most of a post that I did earlier. I hope this makes sense, but it involved day trips from Tokyo.
I am first going to recommend that you get the Tokyo Wide pass to pay for three days of travel, possibly including transportation either to or from Narita Airport, if you are flying in and out of there. This will get you to a ski resort.
So... you can either get three day trips, or, get two day trips, and a airport trip.
http://www.japan-guide.com/e/e2361_06.htmlIf you go to the link, you will find the Shinkansen train lines marked in red. The map will also allow you to click on different outlying towns around Tokyo. I did this, and here are some suggestions.
(1) For Skiing, transportation to and from Gala Yuzawa is covered This is two hours away from Tokyo, so this could be a day trip..
http://www.japan-guide.com/e/e7690.html(2) You can get to Nikko. Edo Wonderland or Tobu World Square work for children:
http://www.japan-guide.com/e/e3879.htmlhttp://www.japan-guide.com/e/e3878.htmlJust north of Nikko is a hot springs resort town of Kinugawa. It is also possible to get one of the Tobu Nikko passes to see this area. So if you end up wanting to do several side trips, you could do this one without the Tokyo Wide Pass.
http://www.japan-guide.com/e/e2358_002.html(3) To see an active volcano, and to get out to the mountains, go to Karuizawa:
http://www.japan-guide.com/e/e6030.html(4) Trains always seem to interest kids. Go to the train museum in Saitama:
http://www.japan-guide.com/e/e6527.htmlAnd, you cannot go wrong going to a town that has a street called "Candy Alley":
http://www.japan-guide.com/e/e6500.htmlCandy Alley in Kawagoe is very close to the Train Museum, so you can probably do both in one day.
(5) I believe that the five lakes area might also be a good choice for a day trip from Tokyo. There is Fuji Q theme park there.
http://www.japan-guide.com/e/e6900.htmlThere are several passes to get here without the Tokyo Wide Pass, also. The link I gave you has a "getting there and around" that you can click on.
(6) Another recommendation that the Tokyo Wide Pass can help is to go to Hitachi Seaside park. Once again, this does not use a Shinkansen train, but I think a five year old will enjoy going here:
http://en.hitachikaihin.jp/guidemap.html(7) The Izu Pennjinsula is interesting. Atami is a great Seaside Hot Springs Resort town, and it has fireworks many times each year. (I wanted to give you both a seaside, and a mountain hot springs choices)
http://www.japan-guide.com/e/e6310.html(8) Finally, the Hakone area is also nearby.
http://www.japan-guide.com/e/e5200.htmlI would actually recommend the Hakone Free Pass, because it includes the transportation costs for the different parts of the "Round Course":
http://www.japan-guide.com/e/e5210.htmlAnd yes... it is possible to spend an entire week at a hotel in Tokyo, and never actually see anything in Tokyo.
I hope this helps.