Engaging children on trips is key to keeping everyone happy, but museums and monuments only hold attention for so long. Kids need to play, preferably with other kids. When your kids' interest wanes, take them to the nearest park or town square to meet local kids. They get to play and expand their horizons a bit, and you get to relax.
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In most European countries, once school is out, local kids often gather in public spots like parks or squares to play until dinner time. Take a break from museums and head out there yourself. Even if your children don't speak the language, children are great at finding ways to communicate with each other. Help them by arming them with snacks or cheap toys that they can share with the other kids. Building in some play time for your kids gives them a chance to burn off energy, and they will come away with some memories, to boot.
Tips for Travelling with Kids in Europe [Rick Steves]