Of course any specific recommendations depend on where you are, but generally the most overlooked resources here are state parks. Kentucky and Colorado have particularly outstanding state park systems with many camping options, low prices, beautiful views, and fewer crowds.
For family camping, check out the state parks in your state. Most state parks are well maintained, have great facilities, excellent trails and access to nearby sites and atractions.
Fundy National Park in New Brunswick is an outstanding camping destination, offering something for everyone including wilderness camping, family camping (with showers and bathrooms) and even hotels, golf, and a salt water swimming pool. The the varied eco-system allows you to experience dramatic Bay of Fundy tides, hike to waterfalls and swimming holes, and easily spot moose in bogs.