How long have you known this guy? And how long a trip are you talking about? A weekend would be about as long as you'd want for a first date.
Don't share a hotel room with him. Make it clear that you and he are going to be staying in separate rooms and that you're paying your own hotel, meals and travel expenses, so you're not obligated to him for anything -- and see how it goes. After all, you'll be in a public place -- Disneyland. It should be safe enough. Make sure someone back home knows where you are -- what hotel, what room # -- when you're coming home -- and check in with them every day so that they know you're OK.