There is an iOS app called The Ultimate US Public Campground Project. I've found it well worth its price. The same developer has one called The Ultimate US Military Campground Project that is free. I have no experience with it but have a lot of respect for the data compiler behind both these apps.
The "Ultimate US Military Campground Project" app is using data from this website, with my permission. If you like this free app, please consider making a donation to this website for use of the data in the app.
They also now have a free Macintosh app available using our data.