It's an expression that means situational awareness. In other words, if you do not have your wits about you, that means you are not very aware or mindful of what is happening around you. You are unable to pickup contextual clues or to fully analyze the deeper meaning of sensory information in that environment. For someone to talk about a hotel in that way probably means the hotel was being used for unsavory business dealings and the full of unethical characters. The person without his "wits about him" would have been unaware of those people until after he left the hotel. People that have their wits about them include club bouncers, police, spies, elite athletes. They are fully aware of every movement, every word, and every trend in their environments.