Only downside I can think of to visiting in December is the static (as the air is so dry)

I was there December before last and remember travelling down to Kamakura on Christmas day where we sat on the beach in bright sunshine watching the kites (huge birds) circling above our head. Snow doesn't usually come until later in the month.

For me, 6 days isn't even close to being long enough. Don't be surprised if you're already planning your next visit before you leave.

Tokyo will richly reward you for any research you do beforehand. Unlike most European cities where it's easy to simply stroll around and encounter all kinds of unexpected treats and surprises, Tokyo is a bit more 'tight lipped' about its own delights. The equivalent to that wonderful restaurant you just happened to walk past in Vienna might be signalled by a poster board in Japanese characters on the 7th floor of a tall building in Tokyo - with access provided only be an unpromising elevator. Sometimes a museum is undistinguishable from an office, or from someone's home, or you may never realise that there was an art gallery within the department store you visited.

You've a lot of time to investigate. And there are lot of very informed people here who would be delighted to help you get the most out of this amazing city.