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Bored bunnies are much more likely to be mischievous. They like to explore. So if the underside of the couch, or the hanging electrical cords are not on bunny's approved list, he'll need something acceptable to inspect. Providing a wide variety of stimulating activities will go a long way to keeping bunny away from areas you want him to avoid. Cardboard boxes and tunnels, hidey areas, hay wheels, wicker balls, seagrass mats, willow baskets, timothy hay cubes, empty TP or paper towel tubes stuffed with hay... are all great options for keeping bunny busy. Most of the items pictured here are consumable. Expect your bunny to gradually eat or destroy the mats, cardboard, & balls. Don't let the plastic be consumed, though.
Hay wheels can provide interest just like the paper towel tubes stuffed with hay. Just don't use them as the primary method for providing hay. The effort required is too much for them to get enough hay, but can make a great boredom buster.