Weather app showing wrong location as local?

When my location is turned on, my weather app has been showing "Los Angeles" as my local weather. While I think of myself as a Los Angeleno, it would be more accurate to say I live in Studio City in the Valley, where the temps can be quite different from Los Angeles proper. This would be like someone in Jersey having their weather always default to New York.

I've tried to remedy this by turning off Location for the Weather app, but then it oddly sets my notice screen widget to Miami, Florida even if I don't have a page for Miami in my weather app. I've tried deleting the Miami page, rebooted the phone, BOOM, my local weather is "Miami" again. It is totally strange. If I could just leave my default at Studio City, that would be more useful but the phone just keeps giving me Miami.