Install fencing around your playground that is at least 5-feet high. Fencing will keep the goats in and keep out any unwanted visitors or predators. Avoid using barbed wire, which can injure your goats.
Plant trees in the enclosure to provide goats with shade. Your goats will try to eat the leaves, so ensure the trees have enough branches and leaves out of the goats' reach. Consider barberry bushes, which have leaves close to the ground that your goats will eat, but which also have substantial foliage above the goats' reach.
Be creative with your goats' toys. They will likely enjoy a large pile of rocks on which to climb, tires on which they can jump, and recycled plastic drums, which they can use as a tunnel.
Put some grain in a recycled milk jug, and give it to your goat. Your goat will spend hours jumping on the jug, throwing it, twisting it, all in attempts to get the grain.