My answer is: Anywhere they want to lay eggs. Usually, mine make a little indentation in the straw of their nighttime shelter. When they dash out in the morning, I hunt through the bedding for eggs.
However, the girls who didn't lay before daybreak seem determined to find the most remote, hard-to-reach places possible. That would include the back of the hay shed, cleverly hidden behind piled bales, and underneath the large amsonia plants, behind a wooden-rail fence. Once in a while, I'll find one just lying out on the ground, near nothing.
My best strategy, since mine seem to all be morning layers, is to check the shelter, watch carefully when one of the girls seems to be missing from the group when they get out for the day, and begin the egg hunt. Even when the chickens coops are open, I have never had one lay in a nest box. That would make my task way too easy!
On the other hand, duck eggs are both beautiful and tasty. So, a little extra work on my part is worth it. Good luck with yours!