Hi most-helpful JC and Edouard!
I found what I was looking for at weather.com. Here's the link:
http://www.weather.com/weather/wxclimatology/monthly/graph/94563That zip code at the end of the URL is for Orinda. Just change that zip code to whatever town you want and nice graphs will depict its monthly averages for temperature and rainfall. Other averages available there, as well, like annual averages, etc.
I attached Edouard's monthly rainfall averages (that is, if your zip code is 94563) as an example.
Yes, I'm aware that my original question was asking about "normal rainfall", and I can see that I also failed to specify "monthly", but that's what I meant to ask: Where can I find my monthly averages (or normals). I'm not sure what the difference between "monthly averages" and "monthly normals" would be. I assume "averages" is statistically close enough. But then again I may assume too much. I never really expected there to be a WeatherCat tag just waiting for me. So these weather.com averages will suit me fine, I think. An array can hold all twelve monthly averages and be called upon whenever and where ever.