Friendship Island is a recent addition, and was constructed shortly after Anger used his override switch to submit a dangerous faulty idea. Disgust was able to stop the idea before the command went through, but it shook up the world's priorities so much as to destroy Family Island as a personality facet. Friendship Island looks suspiciously similar to Family Island with cartoonishly proportioned homes and cars and asphalt driveways, but the mannequins inside are all shaking hands rather than hugging.
Comedy Island and Animal Island have always been around. Comedy Island has one big quiet library where hand-picked memories and blueprints are kept, but is mostly a giant construction site littered with ramshackle structures that are torn down and rebuilt every few seconds. Tiny worker ants in hard-hats, hardly big enough to see, build and break down everything with dizzying speed. Sometimes one of the structures is particularly appealing or clever, and the blueprints are then submitted to the library for safekeeping.
Animal Island is a single gigantic hotel the size of a city block, with butlers and cleaners hurriedly working to serve the thousands of patrons within around the clock. The patrons are all (unsurprisingly) animals of various species, from dogs to birds to ferrets. It's the only personality island that has never changed in structure, though new animal customers still come in every day and never leave.
The HQ is a cramped apartment building; the POV screen is a television surrounded by couches, with the command board haphazardly wired up to it. Wires clutter the floor and nothing on the command board is labeled, but Joy and Fear have a good grip on how it works by now.