To rent a hotel room, you must be at least 18, since that is the legal age in the majority of states. The two main reasons for are the hotel's liability and the ability to enforce a legal contract.
Any young adult between the ages of 18 and 21 can run into more difficulty when trying to rent a hotel room than an older adult. Persons who are under 18 cannot rent a hotel room, since it is illegal to enter into a binding contract with a minor. A minor who signs a contract and breaks it cannot legally be held to the contract.