If computers do need to know, then they’ll need to know a specific store with a physical location. That gives you the time zone.
Mapping a location to a time zone seems fraught with peril. I’d store the local time zone explicitly.
Another good example. Arizona doesn't follow Daylight Savings, but the Navajo Nation, which includes the Four Corners area and is in three states, does observe the change.
However the Hopi reservation, completely surrounded by Navajo territory, is entirely in Arizona, and does not observe DST. So it can get quite complicated and it's not enough to say "Arizona doesn't have Daylight Savings Time".
You've never wanted to call a business in another timezone before making the trip out there?
However, if I look up the opening time of a Home Depot in another time zone, I expect the result to be in that store's local time! I'll do the conversion myself. If I get my local time instead, I'll still perform the conversion, and get the wrong result.
You could just decide that any time listed anywhere on the internet should include a timezone... but that would be nuts.