Public campgrounds are everywhere, including inside cities and counties. There are even a few near to your favorite theme parks (such as the Disney, Six Flags, and Busch Garden parks). Unfortunately, they aren't right next door to those theme parks, reducing their appeal for those who wish to use their tent or RV while enjoying a day or two at a theme park. Most of the time, they are at least 10-20 miles away (or more).
Then there is the transportation factor. Most public campgrounds are sequestered away from public transportation, so it's more difficult to catch a bus or commuter train to the theme park. They are also usually not served by the transportation company of the theme park (such as the Disney buses in Orlando, or the Anaheim Resort Transportation System in California.) If you have a towed-car or a tow-vehicle, you can take your car and leave your sleeping rig behind. If you are in a tent, well, you therefore have a way to get to the parks.
Lastly, there is the parking issue and resulting fees. Most of the parks that I have researched (and enjoyed) have a parking fee involved. Many of them have gone to a parking structure in order to hold more cars in the same acreage. Parking ranges from $15 up to about $25 per day, for a CAR. If you are trying to park a motorhome or other extra-large vehicle, you will pay more than that. When you start adding the cost of the extra gas (between the public campground and the park) and then the parking fee, perhaps a commercial RV park or campground that is closer, or even on site, starts to look like a better bargain. Perhaps you can completely ignore the parking fees and just park your vehicle/s for the days you are there and ride public transportation!
But for those who really want to stay away from the crowds and the theme park mindset, these lists will be provided for the main theme park areas: Anaheim, CA; Orlando, FL; San Diego, CA; Santa Clara, CA; Vallejo CA; Tampa, FL; Titusville, FL; Williamsburg, VA; Hershey, PA; Cedar Point, OH, Chicago; St Louis, and a few in Texas. Others may be added as time permits.
Here is a list of Campgrounds near Theme Parks -- Starting in the east and moving (more-or-less) west.
Parks located in Eastern States:
Georgia & Virginia, Pennsylvania, Ohio, Illinois, Missouri,
New York, Maryland and DC
Parks located in the Central States:
Parks located in Mountain States:
Parks located in the Western States: