There are several varieties of blueberries that do well in no-snow climates in California, check with a good local garden center (not a big box home store) as to which varieties are right for SF.

Raspberries in SF, information here:

Here is a link that might be useful: raspberries in SF

I would not recommend planting all three types of berries in the same bed, they have differing needs and growth habits. Because raspberries tend to spread unless restrained they should be grown in a place where they cannot escape or overwhelm anything else. Blueberries prefer acidic soil, so they would be happier in their own bed with a ph between 4.09 and 5. And I always like to raise my strawberries up so that they are easier to pick, because they are so low growing.

There is a new type of raspberry that is both dwarf and thornless, but I've never tasted the berries so I can't say whether it's worth it. Also, with blueberries you need multiple cultivars for proper pollination, it's best to plant at least three different bushes.

Don't know about blueberries, but raspberries and blackberries are extremely invasive. If you want to control spreading please put them in a container or raised planter.
Our neighbor planted them along the fence line between our property and they were rooting underground and sprouting up all over the place on our side of the fence taking over our small planting area next to our patio. We were unable to control it and finally asked if they would remove them and fortunately he did when he saw they were growing much better on our side than his. They were still sprouting after he removed them and a total PITA. Took about a year to finally kill thm off with Brush B Gone spray.