Good places to travel to for just a day or two in Japan

[wriot]

Hey there,

I've been living in Tokyo for a few months but been very busy with work so I've not really had a chance to get out of Tokyo. I have a few free weeks coming up and I want to make some day trips to some interesting spots (probably by shinkansen). I am already going to Hakone but I was wondering if any of you had any other suggestions? Also what's the best way to buy tickets for the shinkansen - does anyone know if there is a rail pass you can buy which lets you make lots of trips on the cheap? I quite fancy the idea of just getting up and saying "hey today I am going to such and such."

Cheers for any help you can give!