I've got a variety of perches placed at a lot of different heights in the run, their old brooder -- which is a 2'x2' box with a window on one side and a door on the other and a hinge opening top (for cleaning), and a bale of straw which is currently sitting partly on top of the brooder and partly against the side of the run to create something of a tunnel around the brooder. They LOVE the tunnel, and they also seem to love being able to fly up to such a wide range of heights -- they can jump up as low as a foot onto a perch, or as high as about five feet. I also toss a lot of straw and leaves around the run, which they like to scratch at to find tasty bits, and lots of veggie scraps they can work on.
I would just put out there, though, that it can be easy, in my opinion, to misread their behavior as boredom. For example, while humans seem to have a hard time just sitting in one place and experiencing life as it comes, I haven't observed the same discomfort in most other animals. As long as they have enough space to stretch their wings a bit (literally and figuratively), I suspect that when they are just sitting/standing/lying about, they are simply enjoying life in a way many of us have forgotten how to do. (In my experience, when they are bored, they begin to take it out on each other.) And when they get all crazy excited when they see us, I suspect it is often just because food is such an appealing thing and we so often come to them bearing it.