Tom has some good advice over in the left column, but here’s my top tip for you as someone who used to live in a hurricane zone.
You can skimp on almost everything else (except a safe place to be) but you cannot manage without water. It’s also a huge boon to you in a lot of ways.
You need it to drink and you shouldn’t assume you’ll be able to drink what comes out of your tap. The safety of our municipal water supply depends on it maintaining positive pressure. Meaning that your water company keeps sufficient power and resources to keep the system pressurized well enough that water seeps out of the system rather than in from surrounding ground… which may or may not be safe without boiling. Which, if you’re without power, you may not be able to do.
So fill some containers. You don’t need to brave the crazy grocery for bottled water. In some ways you don’t want to – fill some junky old containers, leaving some room for expansion, and put them in your freezer. They’ll help keep it cool for any period of time your power is out and you can drink it. You can survive without food for many days, but you need drinking water.
Out of room in the freezer? Put them in the fridge. Same principle. Your physicist buddies will tell you that it’s water’s high specific heat, allowing it to resist temperature changes, which helps you here. Once you cool it down it tends to stay at that temperature, keeping the things around it at a similar temperature.
Don’t have tupperware? Zip-seal bags work too if you’re sufficiently gentle with them.