Sleep does actually occur during overnight trips, and other myths about camping from a camping family.

Start with a map, and show it to the kids. We always do well at State Parks, which allow everything, within reason, and the costs are low.  A pond, a playground, some wooded or grassy trails and dirt roads to bicycle are the minimum features for a campground.  

When the driving distance is kept to under 3 hours, you can head out, stop for lunch, make camp and still swim on the first day out.  If the Friday night traffic is daunting, we have been known to stay over at a motel, and approach the wilderness the next morning.  

What chores, or camp tasks are appropriate for kids?  Well, they can all carry stuff; handed out according to carrying capacity. They usually help with the tent. We use multiple tents these days, and this system has encouraged independence, and better sleeping for everyone. My old 2-man tent, which once sheltered us young married's, is now either the girls tent, the boys tent or sometimes just Mom's space for reading.

Ground rules: On bikes- mostly I am concerned about the roundabout camp roads- which appear kid friendly and are potentially dangerous; think of oversized campers, trucks and strangers, and just getting lost. Some of my methods: jump on my own bike to chase them around, intercept them, accompany them and sometimes act lost, so that they show me the way home (act?) I also give out maps, review stranger safety rules, and bring walkie talkies. 

Playgrounds: set up usually next to restrooms-they are definitely not a danger-free zone. Too many kids who are strangers to each other, and not enough adults. Take your kids there, and join in or sit nearby. If you have pressing camp chores, make sure to check back regularly on the playground action, and review the ground rules.

Hiking: Start with a map, or guide. The rule of thumb is that kids should be able to hike their age, after age 7. While a photo stop, scenic or interesting point is the stated goal, I have found that the little stream crossings, rocky caves, or pond side stops are often the highlights.  I try to estimate the time that the kids will tolerate, and turn around at the half way point. The return is plenty different enough.