I have a 1/3 acre fenced in back yard which is part woods & meadow, part grass, part woodpile, part terraced decorative planting area and part under the deck. The coop's against the woods. It is does not have an attached run or would be comfortable for so many in what is really a sleeping coop. (pic on my page) My 12 chickens have access to the whole thing except up onto the deck.
There are a few plantings I've had to put chicken wire around, mostly my clematis. So far they've avoided the hydrangeas, wisteria, marigolds, lavender, basil, daylilies, hosta, asters and roses. They can't get at my tomatoes, but they've love to.
They use part of a terrace as a dust bath, so whatever was planted there is gone. In the early summer they decided to take naps under the peonies and almost destroyed them by wallowing and taking dustbaths. I used black plastic stakes and string to keep the peonies upright. They didn't eat them, just loved the shade.
Under the deck I have their straw bales stored under tarps, with part of a broken bale strewn around for them to have fun with. They take shelter from wind and rain under some 4X8 sheets of tar paper covered wood siding.
I think part of the success of having my girls in my backyard is there is a lot for them to do. Lots of places to scratch, explore, discover bugs and worms, and do general chicken stuff without it causing mischief or create havoc. I'm not trying to have a Good Housekeeping backyard and coexist with chickens, though it was pretty close to GH before the chickens got dawn-to-dusk free range capability.
Not sure what next spring will be like, when the masses of daffodils, tulips, and grape hyacinths emerge again. They were too little this spring to be interested. This year they may be chicken yummies. The majority of my GH-type plantings are in the front yard where the girls can't go.
I might extend their fenced area further into the wooded area and close off their access to the terraces. I use 2' high green rabbit fencing. Since the girls' wings are clipped they have trouble flying up over it when they're close to the fencing.