Ah, I had a Rosie dog as well, she was a medium sized mutt walk-on (just showed up one day). My current dog is Frankie, another medium sized mutt from the local dog pound, and she is getting up in age (12). She has lately developed a bunch of those old-dog fatty tumors (lipomas) but otherwise seems to be holding in there. I do give her joint supplements and fish oil, and wet her food down with an herbal tea blend I concoct. She travels with us, which is another reason we like an RV.
Re campsites: some parks will let you reserve ahead of time and you can usually pick your spot from afar. Most have web sites with site maps to help you choose. I know the Washington State Park website even has a photograph of each campsite, which is helpful when choosing ahead of time. I don't have much experience with RV parks, we refer to those as 'cordwood camping' and only use them as a last resort. I find them more expensive than state or county campgrounds, way less privacy, often no firepit or even a picnic table, many times just off major highways -- but with the advantage of laundry facilities and full hookups, usually a small store. They are plentiful and those giant RV books seem to focus more on RV parks than campgrounds. My guess is RV parks are a good choice for one-night lay-overs, or for those who will be using their RV as more of a motel alternative and will not be hanging at the park all day.
We have friends who have taken a couple cross-country trips towing a small trailer. They park for several days in campgrounds just outside major cities, then use their tow rig for day-trips to museums, monuments, galleries, and such. Suits them well.
For us, the campground IS the destination and we often spend a couple days exploring the immediate area before moving on. Sometimes our total miles driven may be less than 100, but even that short drive can be a total change of environment.
We rarely plan ahead, which can be problematic. We do now have a cell phone with internet connection, and that will likely change our habits.
So far, knock on wood, we have not stayed in the parking lot of a WalMart! No offense to those who travel that route, it can certainly be a money saver. Just not very picturesque. We have occasionally stayed overnight at rest areas, typically on a long drive-day when trying to burn some miles - arrive late, sleep, leave early. They can be noisy, especially if you are near a refrigerated big rig that runs all night.
Do keep us posted on your trip, I am making notes of good campgrounds all over the U.S. in the event we take a cross-country trip.