My rabbit lives in my kitchen (which is part of my open plan kitchen/living room) but she has a stair gate which stops her going into the living room section – hard to explain!
She has a small indoor cage which is open all the time for her to go in and out of – it has a litter box with hay in, her food and water and her bed box (a cardboard box with a towel in that she uses to sleep in)
Then in the kitchen she has lots of cardboard boxes to explore, some plastic tunnels, some toys, a wicker dog bed with a blanket in, an wicker car basket with blankets in that she sleeps in sometimes, and a soft squishy dog bed, oh and another litter box.
When I am at home with her she has access to the living room section as well – but only under supervision as her litter box habits aren’t 100% yet and I’m fed up of having bunny pee on the sofa!!!
I’ve only used open litter boxes for Pancakes, but I’ve seen posts where other members use them succesfully, I think it will depend on your rabbit but they can be great for keeping litter (and wee) in.