First of all...
Zombies don't sleep! And secondly if you have weapons and ammo, home is a reletively safe place 'cause you'd know the entire layout of your hous better than a mall. There would be a shitload more zombies at a mall than your house. Also once you're in the mall you're likely to be surrounded by the time you've got supplies that you are apparerently low on. Once you're surrounded in a mall, inside or out, you're preaty well screwed 'cause the gates at a mall aren't exactly the strongest. Plus at a mall there are a lot more places where zombies could enter and a lot more ground to cover. If your alone, home would be the best option.