The picture you included is of the giant house spider which is found in Oregon and Washington, but not in California. But several other spiders that do occur in California and enter home could look very similar to this one. These include several species of grass spiders (Agelenopsis spp.), the closely related barn funnel weaver (Tegenaria domestica), some kinds of wolf spiders (family Lycosidae) and a few others. I have included a link to a webpage of some of the common spiders of California that you can check to see if any look closer, but it also could be something that is not included there. http://www.spiders.us/species/filter/california/
Of these, I think the grass spiders and barn funnel weaver would be ones that more likely would enter into homes and buildings, although these are usually not quite the size of two quarters. So why are the spiders coming to your sink? They could be male spiders that have abandoned their webs and are wandering around seeking females with which to mate (usually happens during the summer and fall). The females usually stay with their web and make the males come to them. Wandering males frequently enter buildings and homes during their wanderings. Some of these could be female spiders that are also seeking better places to live because of the hot, dry, draught conditions. They are not coming up through the drain, but rather entering through cracks under your doors or around your windows. These types of spiders are mostly active at night, so that is when they are wandering around your apartment. So what does your dirty sink offer them that your clean sink doesn't? Most likely water. The draught in California doesn't affect just people, but spiders too. And the inside of your home can be just as dry, if not more so, than it is outside. Normally spiders get most of their liquids from the insects they eat. But wandering males seeking mates often don't eat. So a thirsty spider stumbling across even a little bit of water in your sink, might be inclined to hide there and enjoy the extra humidity. And it may be that once in the sink, the sides are too slippery for the spider to climb back out. When there are no dishes and the sink is clean, there is probably no standing water there to attract them and they are more likely to pass the sink by and thus not get stuck there. Since you didn't send a picture of the actual spiders you are seeing, it is possible these could be completely different types of spiders. However, whatever they are, my best interpretation of this is that they are following a similar behavior of seeking out water.