No, they don't have "cubbies" for people to put their stuff in, at least none I've ever seen or heard of. People either take their bags with them because some rides have a place to put stuff at your feet (not rough or intense rides) or hold on your lap, or lock things in a locker. Sometimes people with strollers will leave things on them, although that is risky too. I usually take a fanny pack and just adjust it on my waist so it's not in the way of safety bars. In fact, having been to Universal Hollywood, Sea World and a few other parks, I dont' ever remember seeing cubbies for anything other than shoes for kids play areas. What parks have you been to that have cubbies?