Dont forget to get the Hakone Pass if you're staying a night there. There's a good route which I took last time. Can't remember where i saw it. I think it was recommended by a free tour booklet at the airport.
1. Shinjuku to Gora via Shinkansen (Odakyu Limited Express "Romancecar" | Odakyu Electric Railway)
2. Gora to Owakudani via ropeway (scenery is fantastic, dont forget the black eggs!)
3. Take the pirate ship to travel across Lake Ashi to Motohakone (note that this is the 2nd stop)
4. At Motohakone you can take bus to go to a few onsens of your choice.
5. After staying overnight, you can visit Gotemba premium outlet if you're into shopping before you head back to Shinjuku by bus late evening (more convenient)
if dont want overnight stay can? what is the latest bus back from fuji?