As for the California SF Bay area, weather prediction is mostly useless, day to day weather prediction is wildly inaccurate. I think just on Friday there was a prediction that we were going to have a bunch of fog through Tuesday, and it was clear the next day. Wild storms will be predicted, and then never appear, and other times weather that was going to hit Oregon smashes in to the bay for three days. Many times we've gone out sailing expecting calm forecasted weather (Mother's Day 2016) and got 25mph winds and other times we went out expecting forecasted 15mph winds and it was closer to 6-8mph.
My guess is that the lack of HD weather radar in the pacific and the complex topology of the coastal areas and the bay, and also the chaotic interaction between ocean and inland weather systems make for a much more challenging forecasting system than doing forecasting of the plains states. The unique geography of the golden gate being a venturi tube between the low pressure 55F/13C pacific ocean marine layer and the high pressure 95F/35c central valley some forty miles inland creates what the local slang describes as "the wind machine".
Its amazing how far we have come in weather prediction. A few decades ago, 5-day forecasts did not exist and now we get 10-day forecasts that are reliable enough that we take it for granted.
In my experience, nothing beats getting the forecast straight from the horses mouth (NWS that is). Some companies are notorious for producing 30+ day forecasts, which cant have any meaningful levels of skill.
I never understood why NOAA/NWS didnt just create their own mobile app. I use Wx[0], which parses NWS data directly and can be found on f-droid.
There was almost legislation to stop them from distributing data to the public directly, because then companies can make more money doing it.
This is the page that I check every morning: https://www.wpc.ncep.noaa.gov/qpf/qpf2.shtml
but compared to a smaller city also with microclimates on a large body of water the prediction for San Fran is 15% better - https://www.forecastadvisor.com/Minnesota/Duluth/55811/
Big storms are often exaggerated, though I suspect that's because the risk of flooding, ice and other hazardous travel conditions are serious enough to be overly cautious.
We had predictions for major snowfalls a few times, and every time was completely overblown, and then one hit exactly as predicted. Definitely glad I wasn't on the road that evening.
https://mag.ncep.noaa.gov/model-guidance-model-area.php
Select GFS (Global Forecasting System, the usual model) and NAMER (North America), then Precip P06 (six-hour precipitation accumulation), and then Loop All.
Over time, you learn the behavior of the models; for example the GFS's longer-range predictions tend to overestimate peak rainfall from super heavy storms (it'll predict three inches and we'll get one).
It's not as convenient as Wunderground but it's data straight from the source.
Other occasionally useful models are the NAM (shorter range and limited to North America) and the HRRR (high time resolution but very short range).