Close to running water is important.
Some places you have no choice as the flat places are few or covered in 3-6 inches of water.
I try to be in a place that I think won't inhibit my hunting, far enough away from where the animals would have gone if my camp wasn't there, but I like to be 30-60 minutes hike from where I want to be, come first light. You're basically guessing at that point though. I've been where I thought I was 3 miles from elk and listened to bugles all night and you hear those stories over and over of guys making camp and listening to elk all night.
Consider the wind in the AM as you'll generally have wind in your face going uphill in the AM.
Which is why I'm in timber. I like a tree to hang a food bag in. I like being in trees to spread the lightning risk around. They block the wind too, and make the rain fall more vertical than sideways. Young trees are better than old trees because they are less likely to fall and kill you while you sleep, and they weigh less. I double make sure no dead trees are around.
I put camp up high because it's warmer for sleeping than camping down low, and I can get by with a lighter bag and pad.
1. Safe and free from beetle kill trees. 2. Dry 3. Reasonably flat 4. Near water 5. Near elk
This past fall I camped "in" elk a couple of times and was really surprised at how little it bothered them. I walked up a hill one morning in the dark, broke a stick, and cow called, because the bull was 200 yards from my tent and I wanted to sound "like a cow." He came to 10 yards and stood there, but it was still pitch black and I had no shot. The elk walked off and I called him into 50 yards less than an hour later 600 yards from my tent. I camped with the elk herd several times last fall and got into elk each and every day I camped near them. It may have been a fluke, tons of elk around, or just maybe I had "rookie luck." Either way, I would do it again and would hope for similar results.
More proof that a dummy in the woods is more dangerous to himself than the Grizz he walketh amongst.
Few years ago our camp was in big live aspens. Safe, right? So we had a big wet snowstorm, leaves were still on the trees, and a huge branch broke and plunged right through my tent like a sharpened spear, where I'd been laying about 30 minutes before.
Carnivore's point about temperature is right on. Being in the bottom of a drainage can be 10-15 degrees colder at night than uphill a little on a bench.
I have a spot in Wyoming where it is an old mule deer bed. On a flat spot at the upper lip of a creek bank, but slightly below game trails. I had elk come in on the trails as I was trying to sleep and they never spooked. Close enough I could here them breathing. Needless to say when the bull bugled 20 yards from my tent, sleep escaped me! They didn't have a clue.
Worst spot, NM hunt. I was camped in the upper reaches of a big meadow. First night, I had a big herd come into the meadow. Had Bulls bugling and chasing, cows chirping. They ran so close I thought I was going to get trampled to death.. Unfortunately I killed the spot. Mt scent continually drifted into that meadow and elk sitings went down to nothing. On top of that, I exper such a wind storm, my tarp smashed my face all night long.. Elk were fun to listen to at night, but that didn't punch a tag.
Definitely not the lowest spot around. A bench of some type, where cold air won't pool at night and freeze me out.
Bake
They don't mind toilets at all. Only the smell of the guy using it.