You can have your gun in a shut not locked glovebox and transport it to your rented room if you are not otherwise prohibited. I'll cite the law in a moment.
SECTION 23-31-230. Carrying concealed weapons between automobile and accommodation.
Notwithstanding any provision of law, any person may carry a concealable weapon from an automobile or other motorized conveyance to a room or other accommodation he has rented and upon which an accommodations tax has been paid.
SECTION 16-23-20. Unlawful carrying of handgun; exceptions.
It is unlawful for anyone to carry about the person any handgun, whether concealed or not, except as follows, unless otherwise specifically prohibited by law:
(9) a person in a vehicle if the handgun is:
(a) secured in a closed glove compartment, closed console, closed trunk, or in a closed container secured by an integral fastener and transported in the luggage compartment of the vehicle; however, this item is not violated if the glove compartment, console, or trunk is opened in the presence of a law enforcement officer for the sole purpose of retrieving a driver's license, registration, or proof of insurance; or