They live in a World Tree, a gigantic tree that was turned into a large city! This room in particular belongs to Riddle, and he lived in Central Undercity, which is mostly shrouded in darkness so it has a lot of mushrooms :3 !
Rhyme doesn’t actually have a room, his people who live in the Canopy don’t tend to have possessions of any kind, which includes personal homes, but he would visit Riddle a lot before they eventually moved in together!