In the airport and car it must be unloaded and in a fastened case. A motel room is considered your dwelling, so you can do whatever you like inside your room.
Heres the Minnesota law, first the exceptions:
https://www.revisor.leg.state.mn.us/bin/getpub.php?pubtype=STAT_CHAP_SEC&year=2007§ion=624.714
Subd. 9. Carrying pistols about one's premises or for purposes of repair, target practice.
A permit to carry is not required of a person:
(a) to keep or carry about the person's place of business, dwelling house, premises or on land possessed by the person a pistol;
(b) to carry a pistol from a place of purchase to the person's dwelling house or place of business, or from the person's dwelling house or place of business to or from a place where repairing is done, to have the pistol repaired;
(c) to carry a pistol between the person's dwelling house and place of business;
(d) to carry a pistol in the woods or fields or upon the waters of this state for the purpose of hunting or of target shooting in a safe area; or
(e) to transport a pistol in a motor vehicle, snowmobile or boat if the
pistol is unloaded, contained in a closed and fastened case, gunbox, or securely tied package.
Here's the carry law:
Subd. 1a. Permit required; penalty. A person, other than a peace officer, as defined in section 626.84, subdivision 1, who carries, holds, or possesses a pistol in a motor vehicle, snowmobile, or boat, or on or about the person's clothes or the person, or otherwise in possession or control in a public place, as defined in section 624.7181, subdivision 1, paragraph (c), without first having obtained a permit to carry the pistol is guilty of a gross misdemeanor. A person who is convicted a second or subsequent time is guilty of a felony.