I've gone down the prepper rabbit hole and have walked back a bit from building the underground fallout shelter.
In a perfect world, if you aren't constrained by professional responsibilities to stay in the area, bug out. The money you put in to a storage unit (monthly bill) the items you buy to put in to storage unit (money tied up which can only depreciate unless you ever need it) can be put in to an emergency go bag as cash to pay for expenses if you have to leave the area. Keep an active credit card with no balance so you'll be able to pay for things like hotels or gas assuming they still have power.
Figure out which of your friends and family are willing to host you in event of emergency and build your evac plans around that.
Be physically and mentally prepared to leave too early rather than too late.
A few years ago right before Hurricane Sandy, I had a friend who lived next to the Hudson River in NJ who called asking for advice on what to do. Wife had just given birth to their second child and was reluctant to pack everything up and go. I asked him how they would get to the hospital if the streets were flooded?
They discussed and packed up the essentials and spent a long weekend at State College where his sister was finishing up her Master's degree. Burned up some hotel points for a stay-cation and didn't get so much as a raindrop.
Came back a few days later to find neighbors who'd been stranded in their apartments because the streets had flooded their cars, no power and no ability to go anywhere.
As for the storage unit if you go that route, in addition to the excellent suggestions already mentioned. Be liberal with desiccant to minimize mold and lay out plenty of bug and mice poison.