I have a hedge of forcynthia (sp??) down one side of the property, and they LOVE going under that. We moved here last year, and that hedge hasn't been pruned in forever, so the limbs hang down. It makes a neatest tunnel under there for them. Just hope they don't lay eggs there, or I won't be able to get to them. They also LOVE the holly bush hedges, and have lots of dust baths under there.
For inside the run, I planted a red bark dogwood. It's still living so far. I also planted a burberry bush in the quail pen. Though I don't have any quail now. Our rabbits have enjoyed playing in that pen, and hiding under the bush.
I'm thinking of covering the run with some type of vine this fall, but haven't decided on what yet. I also have to be weary of raccoons being able to climb in so remember that too. Hoping that with my coop locked up everynight I can keep them coons away.