Even for adults, the dark can be intimidating, even in your own backyard. Pick a clear night with a full moon, and the kids might be a little less likely to scare themselves silly with ghost stories.
And certainly try to plan the night around a cool astronomical event. In the Northern Hemisphere, the Perseid meteor shower happens around August every year, and little campers will be treated to 50 to 100 meteors per hour. Expect a late night, though, as the show gets better after midnight and is best in the dark hours before dawn. If you're camping in the Southern Hemisphere, you're probably doing it in the warmer months there; try looking out for the Geminid meteor shower, which comes in roughly December and follows a similar pattern to the Perseids [source: EarthSky]. (Dark sky devotees can also catch this show in the Northern Hemisphere, too.)
If you miss a meteor shower, don't worry: You can always drag out an astronomy book and work with the kids to pick out a constellation or two. Have them try to do as the ancient Greeks did, and find pictures or stories in the web of stars. If all else fails, try to spot shooting stars and satellites.