My own rules (most of which have been posted in one form or other above):

I look up to avoid "widowmakers," whether large dead branches or nearby dead trees.

Pitching fairly close to a tree canopy helps avoid tent condensation, particularly on frosty nights. However, if it has rained hard, the trees will drip on the tent all night even if the weather has cleared.

I look for a site that will not become a lake in a cloudburst. Ignoring that rule is how I discovered that a soggy synthetic bag is no warmer than a soggy down bag!

All things being equal, I'd rather be on duff than bare dirt. Pine needles are easier to clean out of the tent the next morning than is mud. Grass is great, but in order to avoid environmental damage I avoid it unless there's no other place to go. If I have to camp on grass, I pitch the tent at bedtime and take it down as soon as I get up to minimize trampling time. And I never pitch a tent on or where I'll be walking or sitting on mountain heather, which is very easily damaged by being walked or sat upon.

A ridgetop campsite can be lovely in nice weather but highly dangerous in a lightning storm. In a storm, you also don't want to be close to a single or a few tall trees, or out in the middle of a meadow where you're a high point.

A place where the surrounding bushes have leaves of three (I'm thinking of a campsite on Big Sur) is not a great place to be, especially for those who have to make middle-of-the-night excursions.

If you're tarping instead of tenting, you don't want to be within a half mile of the giant anthills I found in the American River valley on the east side of Chinook Pass in Washington. The anthills were taller than my then 5-year-old grandson, and ants were everywhere!

In the Cascades, with their luxuriant undergrowth, very often the only tent site you can use is whatever you can find with room enough for your tent floor, especially on a holiday weekend.