Think about what a little kid would want - a telescope!
If they are showing an interest in astronomy, then a telescope would be the way to go, in so far as hardware goes. Binos are a good suggestion, but you need to appeal to their sense of pride and they need something that will make a statement in their mind. I that is the only point of difference I have with what most people have suggested. Binos are good - no argument from me there. But a scope will capture their imagination more than binos, and won't need to hold the scope in their hands. You can follow it up with a modest pair of binos, as these can be used at any time, not just astro, and they don't need to be anything special. Any pair of binos will show more than naked eyes alone.
What scope? A small refractor. Unless they are familiar with scopes, a refractor is what they will associate with 'telescope'. A 70mm aperture is plenty big for them to handle with only a small amount of help from mum & dad if they are little. They will be able to handle it on their own as they grow. A small refractor will be the easiest for them to aim and get used to some of the mental gymnastics the image of an astronomical scope produces. Such an instrument is not too big a financial expense, and if the kid's interest wanes a bit, it can be stored happily somewhere out of the way until the interest picks up again, or can be passed on without any problem.
A scope alone isn't enough though. An astro app is a must for today's kids. Something like Sky Safari is excellent. It will help explain what different objects are. The only down side is these apps rarely, if ever, mention how DSO's actually appear in a scope. So the kid might be expecting to see a fabulous spiral galaxy, because that's what the pretty pictures shows, when the reality of a scope is not even close. This is the single biggest obstacle. The child's own temperment needs to lend itself to being happy with quiet pursuits, as astro is not a "smash 'n' grab" hobby.
Maybe... a planisphere. Might be somewhat obsolete next to an astro app, but they are light weight and less crammed with info than an app. Its simplicity is its appeal. If the scope really grabs their imagination, then a more detailed book/atlas is good too. Something that will inform them more on the technical aspects of DSO's, like size, magnitude, desriptions, etc.
A star party is a good idea too.
We can get caught up with our own experience with things astro. But it can mean that we forget what it is to be a little kid. We need to appeal to their sense of wonder and amazement. It is one of the hardest things to do at an outreach night, to appeal to their wonder and excitement without pushing the jargon and stats.
My thoughts anyway.