I tried this a bunch of times, and I went to the Mermaid Lake (in Jigsaw Puzzle World) like five or six times, and once I went to Day & Night Towers and once Helmet Girl's Balcony. I used the eyebomb so the rabbit was in the same area everytime I did it, so it could be based on where he is? Or it really is random and he just liked sending me to that lake...