I would hold it to around < 350 yds because of the gun. Like BigBulls said, you could take one further, but I personally don't like the 30-06 at long range. Not a flat gun. You go and put a 180 gr bullet on the tip and that thing will drop like rock rolling off a cliff after 400 yds. That is plenty of bullet for Elk and probably too much for a 30-06. It's like hucking a boulder out there, it will drop like a brick, but if it hits them, yes.. it will drop them too!

I would suggest a bullet in the 160-165 gr range. Even that bullet will already be dropping at 300 yds. (6-10 inches). I would site it in at 250 yds and go from there. That gives you some room at 300 yards to still hold a little high, but be confident. The 30-06 is a great all around gun, but just doesn't hang with the magnums at long range.

If possible or someone in the family has one. Go shoot a 7mm or 300 win mag and compare the drop at set distances. You might end up buying you a new Elk gun. Better yet, go buy a 7mm Ultra Mag... oh wait... I'll leave that for another day. (look at my signature)