What you describe begs for public campgrounds such as state parks, county parks and COE. If you really need electrical then national forests and national parks rarely provide it. Public campgrounds often have much better public bath facilities than private. Public campgrounds often provide a range of campsites knowing tent campers don't usually need hookups at all. You can avail yourself of those sites if fairly level parking. Big rigs will not often fit. Public campgrounds seldom provide sanitary dumps at the campsite but often provide water. Electrical is usually a $3 to $5 premium. They also buffer each site better with trees and landscaping away from your neighbors. The "resort" facilities are elsewhere in the parks and are more adult if you like nature.
Private campgrounds if they are decent usually provide full hookups and have sites way bigger than you need for parking but skimp on overall space. In other words you neighbor's rig could be 10 feet away and their picnic bench right next to your rig. They provide the community facilities but since most campsites are meant for big RVs they actually skimp on the public bath facilities. In other words they cater to totally self contained units. Cheaper private campgrounds that can compete in price with public are often temporary worker ghettos of semi full-timers. Many private campgrounds also have seasonal by the month or winter retiree campers that settle in to live not camp per se. Those types of campgrounds usually have less desirable sites for RV tourers looking for a short stay.
A third option is building an RV that is self-sustaining so you can camp anywhere or boondock, dry camp or off grid camp. A Class B is ideal in that it can take advantage of the many national forests campgrounds that were originally never intended for motorized RV camping. So many of them have a 22-26 foot limit and they ain't lying when they say that. In our upper Midwest of Minnesota, Wisconsin and Michigan they are the best campgrounds for quiet getaways.
The best time to tour is spring and fall. Then private campgrounds may be amenable to desiring you with plenty of space available at a reduced rate.
