By far the best kid-friendly museums in the world are located in the U.K. We moved here two years ago and are amazed by the number and variety of "family activities"--backpacks, treasure hunts, art projects, etc--on exhibit at all museums every weekend, usually for free.

Also a tip for those wanting to introduce their kids to "Culture"-start early. If you take kids to museums when they are still babies, they'll come to think of it as normal and even fun by the time they're a bit older.