Good boondocking sites are a learned skill. Experience tells you where you'll find good spots. Google Earth is the ultimate map, but you'll need Internet access. "Mapster" has excellent topographic and road data and works offline. Free, too.
BLM lands are an excellent resource. I'm no lawyer, but it seems that camping is largely unrestricted. Maps showing the extent and boundaries of these lands are invaluable.
I use infrastructure sites frequently. Cell towers, microwave towers, power transmission lines all have access roads and even if you wind up camping just outside the security gates, you're on public land and you won't get chased off. All provide the three basic requirements: Quiet, Dark and Level.
Invisible is good. Hide. If they can't see you, they can't bother you.
1. Areas around Page, AZ
Walmart lot in town. Marina parking lots.
2. Bisti Wilderness
No idea
3. Ship rock
Native reservations all around. Boondocking difficult
4. Monument Valley
Native reservations all around. Boondocking difficult
5. Factory Butte (near Hanksville, UT)
many small roads into the desert near Hanksville. Otherwise, Capital Reef has a superb campground. Burr Trail and Waterpocket fold has campgrounds.
6. Taos, NM
eastward towards the mountains gets you off the tourist trail
Like arlon, I frequently hide in plain sight. Commercial parking lots, church parking lots (except Saturday night!) casinos, shopping malls, hospitals, anywhere vehicles are likely to be parked overnight.
Happy Hour, somewhere in Central Nevada.