I lived in a similar situation in Houston suburbs for a few years. The main thing to prep for there was hurricanes. You’d potentially not have electricity for a few weeks, and possibly not clean water (not that the water was ever good there), so that’s what I prepared for.
Take a look at what the most likely disasters are in your area. Power out during cold? Heat? Water has a boil order? Forest fires? And prep for that. For example, forest fires you need masks and a good filter system, possibly a way to seal your windows more securely.
When you say you have food for a week, make sure that is food that you can either prepare without electricity, or that you have a safe alternative method of cooking, and that you have sufficient fuel.
And the best thing I can advise is to dry run it. Assume your biggest local risk is power outage. Try 24 hours simulated without power. You don’t have to turn off the main breaker and ruin everything in your fridge…just turn off EVERYTHING you can, and don’t use electric. You cannot charge your phone, you cannot run the air/heat, you cannot run a fan, you cannot do laundry, you cannot turn on lights, you have no hot water, put some painter’s tape on the fridge so you don’t open it (what I’d do during a short blackout to try to save things as long as possible), you cannot use the coffee maker or microwave, etc., and see what happens. You’ll find out very, very quickly some of the little things you need, that can make that situation much better.
Where I was, somewhat inland and elevated, the worst thing that might happen during the hurricane itself would have been high winds or a tornado. So possible broken windows or a tree falling over on the house. For the worst case there, I needed a tornado shelter, which unfortunately I didn’t have. Coming from the midwest, that always made me a bit nervous, but I had a closet that was central that I’d have used if needed.
The worst things were the after affects…the prolonged power outage during a hot spell with 100% humidity., local flooding limiting critical services access and contaminating the water supply, and dense clouds of mosquitos.
I did actually live there during Tropical Storm Allison, which was “just” a tropical storm, but stalled over the city for two days and dumped record amounts of rain, causing catastrophic flooding. Among many other things, it flooded the major hospitals downtown, shutting down their emergency rooms for months, and destroying heavy basement/bottom floor equipment like MRI machines and CAT scanners. For months after the storm, newscasters would daily remind people to be extra careful as we had limited emergency room capacity, and most patients were (ironically) being re-routed to UTMB Galveston Hospital, which had suffered no damage. It took upwards of a year for the downtown hospitals to get themselves back to normal, and these were large, well funded institutions.
So, I guess the lesson from that story is that the knock-on effects can be difficult to predict sometimes. In general, it is good to prep to not have access to critical services, or at least thing about where your alternatives are if the ones close to you become unavailable.
Oh, and if you’re going to do a test run, do yourself a favor and do the first one on a nice day. Doing it during an extreme is on hard mode, and I guarantee you’ll find a myriad of little things just during nice weather. Also, if your most likely disaster is cold, I’d look into the Buddy heaters. I have both the little and big one, and have used both on power-out cold days. Their downfall is that they add significant moisture to the air, but they do warm things up and are very storable. Purchase with a CO detector, I’ve always run mine with one, never had it go off, but important to have. Also, if you have pets, watch them like hawks while running it as the flame is not entirely covered.
And have fun! Doing the test run is kind of like camping in your house. Neat experience, if you like learning and seeing the world in new ways.