I was thinking of taking the family to Tokyo/Kyoto for 6 days around Xmas...how is the weather? Is this a good time to go? Are things open generally? Thanks!

Most everything is open around Christmas. It is New Years that things shut down.

The weather will likely be pretty cold...grey, rainy or light dustings of snow. Think Seattle.

It is fun in that the Japanese do a lot of shopping and the stores are decorated for Christmas and New Years.

The weather is chilly, sometimes cold at that time of year...if the sun is out not bad, but if no sun then around freezing. Everything is open, as lcuy said. There are lots of decorations. Both Tokyo and Kobe have beautiful illuminations that draw enormous crowds.

Christmas Eve and Christmas are the #1 dates for serious dates and marriage proposals...restaurants and hotels are crowdes, and shopping centers are as well.

When we were first in Japan over 10 years ago, things really shut down for the New Year, but nowadays, most shops stay open. Museums and some tourist sites are closed. Shrines are the place to go on the first 3 days of the year to get your fortune for the year and to pray for a good year.

Xmas--great window displays along Ginza and Aoyama shopping areas. Also they do fancy light-ups near Tokyo station. It's not a holiday, so pretty much everything stays open.
New Years--stores/restaurants close early New Year's Eve. Many sites/stores closed for New Year's day but more and more things open 2 Jan onwards. Meiji Shrine is very popular but gets mobbed.

We went window shopping with our kids in Ginza on Christmas Eve and it was fun. The streets were closed to automobile traffic and the window displays were nice. Not quite up to par with New York City displays, but still fun. The streets were crowded and coffee houses were packed, though. Don't expect quick service at any food establishments. It was chilly, snowed the day after we left.