The yard is a natural place for kids to entertain themselves. Children naturally have a lot of energy, and need to be able to run around after school and on weekends. Landscaping parts of your yard with your children in mind will keep them happy by giving them a space of their own--which just might distract them from the urge to trample the garden.
Garden Stepping Stones
With a little bit of help from grownups, kids can make their own garden stepping stones that will last for years. Buy a concrete mix and add water to it according to the directions. Pour the concrete into a mold, such as a disposable pie tin or pizza box. Add footprints, handprints, marbles or decorative stones, or any other designs your kids want to the stepping stone and allow it to dry. This will let your children constructively participate in gardening and perhaps spark an interest in getting more involved in the future.
Backyard Fire Pit
In many families with younger kids, the summer backyard campout is an annual tradition. If your zoning rules permit it, a backyard fire is a great way to bring more of a "great outdoors" feel to your suburban yard. Use stones, the bottom from the grill, or an old truck rim to create the pit. Place a layer of stones around the top and you're ready to start building fires and roasting marshmallows.
If you don't live near a playground, a swing can do a lot to help kids discharge restless energy and alleviate boredom. Hang a tire or horizontal plank from a big sturdy oak tree to create a homegrown backyard swing that takes up little room.