Between the Colorado Plateau and the eastern edge of the Corn Belt, I'm finding that RV parks range from $5 a night (and maybe free the first day) to $60, that's mixing municipal and county RV parks (not campgrounds) with commercial parks that range from overnight parking with hookups behind the motel or gas station to destination RV parks, but no real resorts.
Campgrounds, about $5 a night to $40 a night, usually around $16-24 for RV hookups, less for just parking, higher for popular destinations. I've been told people pay more for RV sites in very popular beach parks, but we don't do that in the middle of the country and I'm not a park on the beach person.
There are lots of places where you can park overnight for free, and others where you can camp for free a couple weeks at a time, off the grid.
So "average" depends on what you include in the average, and how you weight it, because for some people their average might be about $40 where Francesca puts it, others it might be $60-80 (green fees extra), and for many $0 because they simply don't go places where they are required to pay.
Since you are thinking of snowbirding, that puts you in a category of maybe wanting to be someplace warm at the time everybody else wants to be someplace warm, and staying for a while. You can somewhat boondock that too, if you are willing to keep moving, but many boondock in Long Term Visitor areas where the cost is a few hundred dollars for the season.
Most public campgrounds to not have long term stays, but I know of at least one municipal RV park that allows a small number of seasonals, and a tribal park that has long term winter visitors (though most snowbirds don't consider it a warm place). Long term stays are the business of RV parks, and that cost can range from $100 a month plus utilities to $3000 or more. I see $300-400 being pretty typical for a decent place that has a moderate but not really warm winter, in rural small towns where those same RV parks make most of their money catering to agricultural, construction, and infrastructure workers that leave the parks during snowbird season because jobs are seasonal. Think Cotton Belt, and Delta Country.