I'm particularly interested in the area in and around Monterey, but I wouldn't mind learning about other areas.
Certainly, I've read a lot about beef in California. I know the hides and tallow were important/valuable and that there was a time a great deal was made out of leather. I've read ships arriving in Monterey were very rare in the Spanish era. I know that picked up (along with smuggling) after Mexican Independence.
But what else did people eat? What were the differences in the upper and lower class diets. I've read some about Native American diets, albeit usually from an earlier timeframe, but am still looking for info on peons and upper-class diets. I had the impression meat was not uncommon in a mission-era peasant's diet, but don't know if that's accurate.
What grains were most commonly grown? Did upper and lower classes eat the same grains? I know there were vineyards in the mission era. Olives too, right? I tend to think of those as cash crops, but I don't know if that's accurate. What spices were common? What sweeteners were most common?
Well, I wouldn't say that ships to Monterey were that rare. Richard Henry Dana's Two Years Before the Mast is probably single best source for you on this topic. He was a Boston lawyer who took to the sea for health reasons and served on a trading ship that went around Cape Horn to California. While Monterey and the rest of California were pretty peripheral areas--California is about as far as you can get from the North Atlantic as anywhere on Earth--there was clearly a well-established trade. He mentions running into many other ships there, and California was also connected to Hawai'i by trade and by the New England whaling industry.
To your question about foods, the diets were pretty basic. Yes, beef was consumed by everyone, because the rancho economy of Spanish and Mexican California produced a great deal of it. The missions, pueblos, and (to a lesser extent) presidios also grew corn (maize), wheat, beans, grapes, olives, and a wide variety of vegetables and some fruits. (You can frequently see some evidence of this to this day at missions, where grape vines and olive trees still grow. My local mission, San Gabriel, has some grape vines that are extremely old.) There were no cash crops aside from hide and tallow; California's current role as a massive specialty-crop producer for export markets did not come about the late nineteenth and early twentieth century. At this point you're asking about, California was simply not well-integrated in the global economy to pursue such a strategy.
As far as spices and sweeteners, the missions cultivated honeybees, but probably had to rely on imports for sugar and spices. There aren't local sources of those, and they cannot be grown (efficiently) in California's climate. These elements were most likely the real distinguishing points between upper and lower class diets, to the extent that there was much of a distinction. Upper class people almost certainly got the bulk of the exotic foods like sugar, spices, and perhaps wine.
Dana's travelogue is a good read, I highly recommend it. At one point, he describes the "port" of what is today San Pedro, near Los Angeles. It was three Englishmen living in a shack and subsisting on beans and beef while they helped ships load and unload in the surf.
Another thing you might want to look at is De La Perouse's Life in a California Mission, from a French traveler in the 1780s. It's earlier than you asked about, but a lot of the information about food would be good.