Kyoto is a great place to visit as is the Fuji area. Rail to Kyoto from Tokyo is extremely easy. Just get yourself to Tokyo Station (Bus or Rail) and then buy yourself a ticket on the shinkansen - my guess is that the one way shinkansen fare will be somewhere around $100 USD. If you can get by in Japanese, or if you have a friend there, ask them to find you a package deal (these are really popular in Japan) where the hotel and shinkansen will be a combined purchase. If you do this, you can often times get the hotel included for very little difference to the straight shinkansen fare - but this could be difficult if you have limited ability in Japanese.

Kyoto is also very close to Osaka or Kansai Airport (KIX.) If you can do your flights through there, that would make the Kyoto portion extremely easy. Especially if it is just for a few days.

Hakone is a very popular hot spring area/lake near Fuji, but Fuji will definitely take some leg work to accomplish on a brief visit. If you stay at one of the nicer hot spring hotels in Hakone, you will be able to find a bus service included from some of the suburban Tokyo stations. That equates to getting into downtown Tokyo, transferring to a local train to get closer to the Fuji area, then taking the resort bus. If you do all of the research and book all of the stuff in advance it is easier than it sounds - and it can be quite an experience, too.

Hope that helps.