It must be said first of all that no hike is by definition "suitable for children". Before setting out on a hike, the boy or girl who is about to start walking should already be used to walking in everyday life.
People often get this wrong: a parent is not a child's best friend. A parent has the responsibility of bringing up their children, which means imposing unpleasant things on them too: eat your vegetables, do your homework or simply, as far as our case is concerned, urging them to walk.
Little ones tend to be lazy and listless, and they rarely find any reward in the hard work of trekking. The parent must be convinced that hiking is an excellent sporting activity and that it's also an excellent activity from a cognitive point of view. You learn to make your body work: muscles, balance, the ability to observe. You learn to be immersed in the natural environment.
By imposing small sacrifices, which don't go beyond their physical strength, over time children can discover the positive sides of walking.
From as early as five years old, young walkers can tackle even very long routes, with the help of parents, relatives and friends.
What we'd recommend is to start gradually, with routes that don't exceed 4 or 5 km in total. It isn't a physical problem of endurance. Children recover their strength much faster than adults. A break for a sip of water or a bite of a sandwich lets them get back on their way quickly. 
The real problem is that on routes that are too long children get bored.
When the children are small, 5-6 years old, give them little goals such as looking for stones or sticks. Give them the goal of counting the paint marks you find along the route; these are trivial goals but they'll take up part of their attention. Have them count the flowers, suggest they look for the wild animals of the woods. All this will also sharpen their ability to observe nature.
Teach them the names of the peaks. Of course they won't remember a single one; what matters is that they'll begin to understand that the land is made of peaks and valleys, of hills and roads, of woods and streams.
When the children are older, 7-9 years old, this is certainly the best opportunity to get them talking. Television, music and video games fill everyday life with a deafening, never-ending noise. For once the hike can become the chance to stop and listen to them. Something that we adults, we have to admit it, no longer know how to do.
Get them to talk about their favourite habits. Think you know them? Well, it could be revealing to understand their way of seeing the world.
After taking them a few times on short routes you can, over time, start choosing routes that go even beyond 8 km. Never let them go without a good number of outings a year. This will do them good... and you too, naturally...
One outing worth trying is the hike to Monte Piano with children.