--whoops-- I just re-read your post and noticed you want a AA battery and my recommendation below is AAA. I will leave the post anyway.
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I prefer a fenix E05. Now about $20 or less. Runs on one AAA cell and is not much bigger than the AAA cell.

https://www.fenixlighting.com/product/e05-fenix-flashlight/

Setting Lumens run time
Low 8 15h
Medium 25 4h 15min
High 85 45min

I have carried this light for years and have found it to be well suited to my needs. It has a twisty tail turn on, which many folks do not like. However it find it very reliable and although not as convenient as a push switch, it has not failed in years of constant carry/use.

I use enloop rechargeables which I swap for a fresh one at least once a week just cause it is easy to do and that way I have a fully charged light.

I find the low setting (default at turn on) to be more than adequate although sometimes I put my finger over most of the lens to reduce output w hen I need a very low light level like when using it close to others who are sleeping.

The high power setting is enough for most "need a bright light" applications. This light will get me to my stash of really high powered lights should I need one.

It rides on my key ring, attached with a small "S" 'biner which makes it very easy to remove. I added a pocket clip which I use to clip it to the brim of my hat when I need a headlamp.

On medium power it is bright enough for me to use as a headlight when riding my bike at night.

Bottom line is that for me, it has performed very well over several years and has become so much a part of my EDC that I am never without it. I have several stashed in various kits.

Nomad