I like all of the above mentioned. I always get a copy of Time-out and carry a copy of the A-Z and pick up flyers for deals. I walk everywhere so need good walking shoes, waterproof jacket and backpack. You are centrally located so it will be easy. I prefer Hampton Court to the Tower, you can get an express bus there from Victoria Station. Harrod's and Selfridges are a must for me. I buy packed luches from Tesco or Safeways because I knpw that I am getting someting the kids will eat, that it is clean I am not paying a fortune for it and I don't have to wait.
One of kid's favourite things was/is just to be up top on a London double decker bus. Pick your routes and you get a bird's eye view of the Christmas decorations. When I get tired I take a taxi. I spent years travelling the tube- it's hell at Christmas.

When you read Time Out remember that it also caters to Londoners, my family in London are always trying to get me to do the new stuff, when they forget that my kids still haven't covered the traditional.
http://www.timeout.com/london/kids/

Last but not least you must go to Covent Garden at the weekend- free shows acrobats- jugglers, Punch and Judy. Have a hot chocolate or soup at the restaurant down on the lower level and possible get some great live music.
You can walk from Trafalgar to Convent Garden then up to Picadilly.