Probably a quartz with solar cell. I would choose Citizen for that, nobody has more experience with that technologiy than Citizen, they were the first bringing it to the market back in the 80s. But it is EMP-vulnerable. Keep it in a Faraday cage, and feed it the needed light. These needs vary, depending on watch model and used battery cell. Its said their rechargable cell batteries can last up to 15-20 years.
If you talk about end-of-days scenarios, also two or three simple but well-maintained, well-runnign automatics that are tweaked to run with good preicison. Three watches: so that you can estimate the accumulating error. Cheap: so that you can buy three (different models).
I have two Citizen Solar Quartz's.
LINK. The green one is a Promaster, quite robust, and has 20 bar and a Sapphire, and a sturdy case. They both run sufficiently precise, lose a second or two per month.
I would also prep with lets say two simple 80s-style Casio LCD watches for 20 bucks each, and a can full of battery cells for them. Maybe this is the best - annd cheapest - advice in my post.
Really, not one but two or more watches. One electric for precision, the other an automatic for EMP-immunity.
Well. Prepper's worries.
Other people kill time by solving crossword puzzles.
P.S. It does not hurt to know how to mount and read a solar watch on the ground. Combined with compasses, solar watches in form of necklace miniatures also work.