My ideal campsite is safe, legal, scenic, and free. Remote solitude is a plus.
In familiar territory, I know where these sites are from years of practice. Once in a while I get a surprise because land use policies have changed and I have to cross a site off my list.
I have never knowingly camped where it was not legal. I do not intend to ever get into urban stealth camping. Roadside rests and such places are out for me. I did spend the night at a Walmart once, but it was an emergency when a threatened flash flood scared me out of the desert; that turned out to be a very wise decision but it was not a pleasant night.
One factor for me in choosing a camp: Tigers are pretty noticeable as unusual units. Not good for any stealth uses. I've had people (genuinely interested ones, not bad guys intent on harm) approach me in the middle of nowhere to ask about my RV. A plain vanilla common model of a TC on a common model of truck would attract much less attention.
I keep notes about good sites mentioned in forums and blogs, and those notes help when planning trips to unfamiliar places. I've also used the Free Campgrounds websites, but mostly find those unproductive. Google Earth is great for scouting out sites.
I don't build campfires and I leave nothing behind but a few tire tracks.
Most of my campground stays are dry camping in USFS and BLM sites. I do stay in RV parks where that is the only option acceptable to me. It is nice to have their electricity for my little auxiliary heater.