You can also run a regular airpump off a 12V auto battery & an inverter (or a powerbox). This will last longer than the regular batteries. A small HOB might run for a while with this set up (but not heaters).
You can have several batteries to last you days, or in a pinch, charge up the batteries in your (running) car. <Make sure you know what you are doing if you are going with "naked" batteries ... or you risk fire & explosions! Some powerboxes have capacity to be recharged from a car power outlet. That would be the safer way to go.>
Make sure your main filter media remains wet. <Take the media out & float them in the tank, preferable close to the airpump output so some water movement gets to them.>
It is good insurance to have some Prime (or other ammonia binder) to use if you lose the filter during the storm & ammonia startes to go up.
More problematic is heating .... If you lose heat in the house as well, you might get into major fish loss due to cold. First thing to do is to insulate the tank (wrap in blankets). Some have heat water (in outdoor BBQ, etc.) & either do pwc's with the heated water, or put the hot water in a bottle & put it in the tank to keep the water warm(er). Either way, with an extended blackout, it will be a lot of work checking the tank, changing/heating water, etc. A generator is prob the easiest solution if this is a frequent occurrence.