I keep one of those battery organizers (which I know you don't like, but hear me out!) at the top of the basement stairs, attached to the wall. I like that there's a tester built in. The other big thing is to use rechargeable batteries! Then you never run out! They are a little more expensive, but honestly, I got tired of all the regular batteries running down, and they are such an environmental disaster even if you recycle them (which I do). It's a huge expense over time to use one-time batteries.
I charge them 4 at a time, and put them in the organizer while I charge another set. I always keep a few charged in different sizes (AAA for the TV remotes, AA for the remaining remotes and the old calculator my husband still uses, larger ones for the flashlights). I keep a flashlight or a mini-lantern on each floor. Upstairs, it's in the hall linen closet where I have a wire rack hung on the inside of the door for all the little things that don't belong on the main shelvesshelves - bandaids, ice pack holders, ace bandages, and a few emergency candles (because, you know, sometimes the batteries run out of charge during a power outage). I either hang a flashlight on the rack if I have a loop of some sort, or I use a Command hook inside the door and up high. So that way, all the "emergency" stuff that you don't use all the time is not in the bathroom medicine cabinet or under-sink cabinets, but it's centralized.
I keep old jelly jars or votives and put tea light candles in them - the glass keeps them from blowing out and keeps the flame contained. We live at the end of a power line that leads to a dead end. Anytime there's an outage, we're the last ones to get power back.
So, with a small supply upstairs in the main hall linen closet, a bigger stash and tester with the battery organizer at the basement door, and a good flashlight by the door to the garage, there's something to grab no matter when the power outage hits. Nobody goes up and down stairs in the dark.