I often use churches and fire/police stations on cross country tours. More often than not they're happy to let you stay. Some will even let you use their restrooms and showers. If not they'll point you in the right direction.

I've stealth camped illegally a few times. Often times at campgrounds. Arriving after the office was closed and departing before the office opened. The two weirdest places were both in Wyoming. Slept on the back porch of an abandoned house in Jackson and the mens restroom at the town park in Shoshoni. Parks work well too but make sure they don't have a sprinkler system. That was a terrible mistake.

I wouldn't recommend doing it illegally and have only used it as a worst case scenario.