There are so many wonderful museums in London, so you really need to narrow it down when travelling with kids in order to make it enjoyable for everyone. We chose the British Museum, or as one of our friend's son's pointed out, "The Museum of Stolen Artifacts."
The best way to see this museum with kids is to decide ahead of time what you want to see, go straight to see it, enjoy it, and leave. The museum has a great website, so you can check out what you're interested in and be prepared. (We had five kids with us, ages 14, 13, 12, 11, and 10--not all ours!) We all enjoyed the Egyptian wing with the mummies and the Rosetta Stone. We also enjoyed seeing the Elgin Marbles, as we knew were later travelling to Athens. It was all fascinating, andyet we were in and out within an hour or so. We knew we had many more museum visits ahead in our travels, so we wanted to make it meaningful and enjoyable for the kids.
Be sure to also check out the beautiful library in the center courtyard. We also enjoyed taking the Tube to Covent Garden and then walking to the British Museum from there. There were lots of places to eat, and it was great people-watching. We did get a bit lost, so it's good to have a city map with you.