I would think about taking this to the work camping forum, since that is what this is.
Many public parks, state and Federal, have "volunteer" programs for work camping, in season, pre-season, and post-season. Most commercial RV parks depend somewhat on work campers for help, some asking a certain number of hours in exchange for a space, some that actually pay you a wage for the work that you do.
In terms of your question, the answer is "almost any campground in any state" will offer use of a campsite, or more, in exchange for your work. Almost all of the 3000-4000 of them. If you are putting together a list, find a pre-existing list, then call each campground and RV park for work camping information.
To start with, almost every state park in Oklahoma, almost every recreational access facility in the Tulsa District, USACE, has a volunteer program. Tribal parks, however, work mostly with tribal labor resources.
In Oklahoma, Spring Cleanup is right now. The regular season, needing full-season volunteers, starts in late March, early April. A lot of those folks are already on their way up from their winter positions in the Rio Grande Valley.
Tom Test
Itasca Spirit 29B