I live in Washington, but hunt Oregon. I usually see more activity in the early morning, almost legal shooting time, to noon.
Here is an example of the activity in my area:

It's 0 dark 30 and I am on my way to my tree stand. I get there and it is all cockeyed on the tree, like some one was trying to steal it. I pull my flashlight out and look at the ground for tracks. It is all tore up, elk tracks upon elk tracks. So I find some cover and wait about half an hour. Start bugling. I get no reply, but 2 minutes later this 6X busts into my clearing. My hunting partners and I have been after this guy for years, but he always eludes us. Big sweeping rack, nice high points. Beautiful animal. Anyway. I knock an arrow, but there isnt enouhg light for my pins. I cant see. So I wait. It's almost light now. He gets tired of waiting and goes off into the next clearing. I decide to follow. As I get closer to the clearing, I am hearing antlers crashing. I pick my way to the edger of the clearing and the sight before me is amazing to say the least.

This clearing is about 300 yards across and about 400 yards long. In the middle are 4 bulls sparing. On the other side is a huge bull with 3 cows. So there are a total of 6 bulls and 3 cows. I look down toward the end of the clearing and see 2 big bucks a for and a spike, and with them are 8 does. My heart is pounding. I turn my attention the the 4 sparing in the middle. They are really tearing up the ground. One breaks from the group and takes off at a dead run, lowers his head and sticks his rack into the ground "plowing", slides to a stop and does it again.

It is now light enough to shoot. So the one closest to me are the ones in the middle. But they are 100 yards into the clearing. Evert one seems to be concentrated on them so I SLOWLY make my way out of my spot to get closer. No one is pay me any attention. Closer, closer til I am 50 yards out. I glance downto the end and the spike is on alert, so I freeze. Still no one notices but the spike. Appearantly he didnt like what he saw, snorted and every animal took off like a shoot, right into the watershed, where it is illegal to even step foot into.

Which is totally ok with me, I was sick to my stomach from the adrenaline rush anyway, doubt I could have kept steady to take a shot. So I guess this answers 2 different threads, "Which is your close but no cigar story" and "Best time of day".