If you only have one week, and that's it, I'd spend time talking with the game wardens and biologists for the area, as well as trying to find some other hunters who might share info.
Other units I hunt, I want to be there later when they are more vocal and when the big bulls have come down from their solo spots because the sounds and smells of the rut are too intoxicating for them to stay solo and/or in their bachelor groups.
Later in the hunt tends to be more running and gunning with more bugling. Early, at least where I hunt, you are much better off sitting water silently and seeing what comes for a drink or a dip or calling lightly and watching for bulls coming in silent.
It also can depend on both hunting and non-hunting pressure. For example in one of my units, I don't want to be there Labor Day weekend because the crowds are crazy. Grouse hunters, hikers, people fishing, and just people driving around in the mountain on 4wheelers make the place nuts and make the elk even more nocturnal than usual. So much of "When" depends on your individual location.
Bake
No doubt sitting water where others weren't hunting can be productive but you have to know where those isolated sources are! To me finding elk is # 1 then I hunt them! Between glassing & calling both during daylight hours & before daylight you will find hunt-able bulls during those dates, it's the quickest way in my experience to find elk!
As you cover ground & burn boot leather it's possible you will come across some great areas with water being used by elk or trails leading from bedding areas to water or feeding areas. Consider sitting those that last couple hours of daylight, that's the highest probability of their use when not far from bedding areas.
ElkNut1
