Under the sink, keep plastic tubs for recycling aluminum, glass, and plastic. Let the kids do this. They'll love it.
They'll even like taking it out to the garage. Really.
And while you're at it, start a composting pail (with a tight-fitting lid) with non-meat table scraps.
While we're thinking sink, let's talk about what not to keep under there:
Do not store poisons, such as cleaners and bleach, under the sink.
It's a bad idea with little ones in your home.
This is not one of those times that you want to have logical stuff (like drain cleaner) handy. Homes with kids should have cleaners and other dangerous brews stored up high and out of reach in the garage.