Get out of Tokyo and get to Bessho Onsen (別所 温泉). This beautiful little village in Nagano-ken is only a couple of hours away by Shinkansen and fulfils the list of perfect weekend away requirements. Forest, serenity, historical sights, bush trails, cute village streets and the nicest people I've ever met. I had one lovely grandma walk me, my mother and my aunt from the station, straight up a hill to the supermarket just because we mentioned we were looking for a snack. She even went so far as to get mildly angry at the shop clerk when she said they were out of onigiri. The exceptional supermarket sashimi made up for it though. She did also happen to recommend her own ryokan upon our departure, but hey. Why not?
And one more thing - onsen, onsen, onsen. It aint called Bessho Onsen for nothing. We did a considerable amount of soaking, and I'm sure I returned to Tokyo reeking of sulphur on Monday. I've got the onsen bug again, and will continue submerging myself in various pools of water until summer arrives and it's just far too hot for that kind of thing.