There are nature walks, programs for kids, and many other organized activities in addition to plenty of opportunities just to look around or get out and hike. And of course you have the advantage of being right in the middle of whatever point of interest it is you're visiting, rather than somewhere on the outskirts as you would be at a commercial franchise-type campground. In the United States, you can make reservations in advance at many national parks with a credit card. Some parks are so popular that this is the only way to get a spot on your desired dates. A large number of state park systems have a similar reservation system.
Many state parks have cabins available.
Some of the best we've found are in the West Virginia state park system. State park systems are also likely to surprise you with other amenities such as golf courses, spas, or swimming pools. U.S. Forest Service campgrounds are another good possibility we have explored. They occasionally have fewer amenities, and not all can be reserved, but the beautiful natural settings can more than make up for this. We just returned from two wonderful weeks in the Canadian Rockies, where we camped at both Banff and Jasper National Parks.