In reply to Jones_88:
I think you should go for the Yatsugatake ridge hike first, for a number of reasons... That one is the simplest logistically, and you're going to be alone and with no Japanese language. It's also the one that will see the most traffic through the winter, so will have the best trace of all them. You'll need to give 2 days to it, the first day to travel from Tokyo to Chino in Yamanashi prefecture by train, then take a bus to Minotoguchi, then walk in to the Akadake-kosen hut. The second day you'll be able to do the hike with an early start, and then walk back down to the bus and reverse your journey back to Tokyo. The Akadake-kosen hut is open all year round, and if you're there mid-week you won't even need to phone in advance. They have staff who speak enough English to understand and to tell you what you need to know about dinner etc...
You'll need to buy map number 32 in the Yama-to-kougen-chizu map series, available for about 1000 yen from any largish bookshop in Tokyo. Once you've got the map, I'd advise you to refer to the article on my site to get the place names in Japanese kanji and then cross-reference them on the map to figure out exactly where you need to go. UKC forums don't seem to support kanji, so I can't type any of them here for you. To get you started, the bus stop at the Minotoguchi trailhead, from where you'll start the walk-in, is in the top left corner of square 7D on the map.
You can check train times in English on www.hyperdia.com, and for weather forecasts take a look at www.mountain-forecast.com/peaks/Mount-Aka-Yatsugatake/forecasts/2899. Consider not going if the wind speed is yellow, orange or red. Green should be fine. Expect a lot of snow at the moment, and dress for very cold temperatures, with a wind chill well below -20C up on the ridge. Regarding boots, you'll certainly want your Nepals to keep your feet warm. Gear-wise you should be fine with a single walking axe and crampons on this route, with a walking pole with a snow bail on it, although be aware that there are quite a few steep and exposed sections with chains on them along the way, which could be iced up. Given your recent surgery, it might be prudent to wear a harness and take a sling and a locker to clip into the chain if you need a rest or need to think.
My book doesn't cover snow hikes, it's a selection of what I regard as ten of the most classic alpine climbs in the Japanese high mountains. So it won't help you directly for this trip, but may be of interest for a future trip, or to give you a flavour of the Japanese high country.
Several people recommended skiing in Hokkaido. You didn't mention skiing in your post, so they probably didn't read it properly and are just posting their own holiday experience... But if you do ski, it's a good recommendation, and you'll find what's regarded as the best powder snow in the world. They've been getting serious amounts of snow up there this winter, so it could be great! Likewise for the same reason, if you decide to go hiking on Daisetsuzan, you'd probably better take a pair of snowshoes with you
Feel free to get in touch while you're in Tokyo if you have any other questions. I'm based in Tokyo myself, and will be happy to help.
Tony