When am I old enough to stay alone in hotel room?

Depends. Are you talking about staying by yourself in your parents' hotel room for part of the evening while they go out, or renting a hotel room all by yourself? If parents' hotel room, it is their decision, based on their impression of how mature & responsible your behavior is, and how safe the hotel is. To rent a hotel room by yourself, you usually have to be at least 18 and show id to prove it.