Though the math says a mall is the safest place, they fail to take into account the large and easily broken windows that face out around many of them, as well as the panes of glass that are to be found in pretty much all the doors. All easily broken, also, malls tend to have way too many entrances for a single person to really fortify and keep secure.
A prison on the other hand. Easily fortified, and as a bonus, some have yards secured safely in the center of them, surrounded by concrete walls, making them perfect for gardens and such to keep up a sustained source of food. Also, you'll have weapons, medical supplies, and even access to things such as machine shops and libraries, both can be essential in a zombie apocalypse scenario. The only downside is the prisoners themselves, which, depending on how far you're willing to go to keep yourself and those with you safe, can be either simple to deal with or quite problematic. Basically, you can either offer them their freedom, hope they either go away from your prison or conform to whatever leadership you have and stay and be productive to you, or, plan B, kill them all, or even use them as zombie bait.