I find potential campsites by going off road on existing jeep trails on Sunday drives on public lands/national forests... Sometimes just driving, sometimes on trips specifically to go off roading on existing Jeep trails; Keep a lookout for fire rings on publiic land and avoid areas with trash piles and obviously homeless long term "campers"....
To get away from the trouble that "civilization" brings, I try to select the more remote and difficult jeep trails. If a stock or near stock SUV/vehicle can easily drive in and out ithe area is probably not a great candidate for a great camping spot.
If there is evidence that the area is frequented by the Party Crowds ... keep on looking.
Be aware that you can drive into situations that you cannot drive out of/
Be aware that getting towed out may be incredibly expensive or impossible... and that vehicle damage is common and rollovers or flops (laying the vehicle on its side) are also possible due to driver error.
You may be hours from help, and without cellular service; if you are seriously injured... or even if you are not.
If you receive several recommendations about an area, by all means check it out; just don't expect better than an average 'camping in a pasture' experience.
You can often tell when you are remote enough by finding areas not covered by cell service and/or wi-fi.
Although I don't usually do more than a short walk-around to determine the tent location; I try to keep a number of things in mind.
I avoid known flash flood areas.
I normally try to put the tent on a gradual hump in the ground (rather than end up with it in a puddle/low place if it rains).
I try not to have it on a hill side that is so steep that I end up in a corner of the tent the next morning.
I try to put the tent into protected areas between trees and far enough from any road. to prevent it being run over if the area is invaded by partying drunk drivers during the night.
I try to avoid the tops of ridges where there is a likely hood of wind
I examine the trees around the potential campsite for lighting damage; it does tend to strike the same areas repeatedly, and I have had electronics burned out by near misses (near hits?).
...I avoid poison ivy patches...
I use a collapsible rake (or at least the side of my foot) to sweep aside small rocks, sticks and pine cones before I lay down the silver tarp that I use for a ground sheet... if there is a sharp root/stone sticking up, I move the tent to avoid it rather than have the floor punctured.
When entering a new area I try to scope out any standing/hanging dead wood; if there isn't any or the area is picked clean of potential firewood I look for an area that is not as over used.
I'm sure I have missed some things but that covers at least some of them...