It's been a long time since I was eleven, but...

For snow, see this: http://www.japan-guide.com/e/e2265.html

Japan is about as safe as you can get. The big risk is that he, being eleven, will wander and get separated in the crowds. Set up meeting places and fall-back plans. Maybe he should carry a copy of the hotel access map and taxi fare, just in case.

One possibility, if you have the option, is to start in Kyoto, an hour and a half by direct train from Osaka's Kansai International Airport (KIX). Kyoto is far less chaotic than Tokyo or Osaka.

Consider a couple of days in Takayama, to see old stuff, and also to experience everyday Japan in a quiet little city (It may be very cold). If there's no snow on the ground there (last year's Snow Hut Festival--whatever that is--was cancelled for last of snow), see about a day trip to Shirakawago where there will definitely be snow. There's a direct train from Kyoto to Takayama around 8:30 am.

As for what to do, check this forum:

http://www.japan-guide.com/forum/quereadisplay.html?0+17332 and this site, which someone in the forum suggested: www.travelforkids.com/Funtodo/Japan/japan.htm

Museums may not be high on the list for many 11-year-olds but I think both of you will like the Edo-Tokyo Museum--remarkable history of the city and great exhibits. Best appreciated after you've experienced the city for at least a couple of days, and seen its sprawl from Tocho (Tokyo Metro Gov't Building).

In Kyoto, I'm assuming he (and perhaps you) won't want to spend a week looking at temples. My favorite sights can be done in a day. Each is different and most would appeal to any age: Ginkakuji, Kiyomizudera, Sanjusangendo and Nijo-jo. The latter may evoke thoughts of samurai and ninja, as might the easy-to-reach castle in Himeji. Bring wooly socks--you go through Nijo-jo and Himeji castle in slippers which they provide.

If you're in Tokyo there is very little chance of having snow but it will probably be a little cold. I plan to be there in the beginning of February 2009 and I fully expect it to be clear and brisk.

We did have snow in Kyoto/Osaka/Nara this February, which prospect I seldom have even for dead winter. If you'd like to go through with a dazzling snow view, you might like to hit a place like Shin-Hotaka (Gifu) from Tokyo, that being a bit of a hassle to get to for a first-timer, though. But if you are a skier, there's Naeba, Zaoh, Shigakogen, Hakuba and etc, etc...

Safety can perhaps be the least common apprehension held by overseas travelers, IMO.

You can go to Tokyo Disneyland or Disneysea if you are disney fans. I am going in January and i will be going to Tokyo Disney Resort for three days and sightseeing tokyo on my last day.