Mac OS Sierra - Weather widget doesn't remember my city
If your Mac is logged in to your iCloud account and you have an iPhone also connected to iCloud, try adding the location into the Weather app on your iPhone.

Weather data is synchronized via iCloud between your Apple devices, and I’ve found that entering it on my Mac does not always push it to iCloud/the iPhone. Then when the Mac reboots, it tries to synchronize with iCloud and deletes the location.