In Kid's Summer Campsthere is information on how to get started looking for a summer camp. In the USA there is a searchable database of camps, including camps for children with special needs. The Kid's Summer Camps article has a link to the database.
The special programs camps offer are not always obvious from their websites and brochures.
In one camp I know about, there is an ongoing program for campers who are developmentally delayed to participate with appropriate support within the mainstream camp program. However, the campers registered through a separate program, not with the camp directly.
When I searched that camp's website, I couldn't find any mention of the integrated program.
The lesson is: if there's a camp you're wondering about, ask the camp director whether their camp has any integrated programs and how to get into them. It may be a multi-step process involving a separate agency.
The same goes for non-integrated programs. For example, I know of a camp where all of the campers are burn victims. These kids look forward to seeing their camp friends every summer in an environment where everyone else is just like them. They have the whole camp to themselves during burn camp.
Again, the camp director has all the information about registering for these special camps, which are not widely advertised to the general public.