I do not know of any downtown. There is a pet store by the Sports Arena. Just a bit north of downtown. Pet Kingdom. Kind of depends on what you are looking for. It seems like a lot of fish and shrimp aren't available in San Diego. Might just be a California thing.
I think you would have better luck find stones up near you. Lava rock and such. Pet Kingdom has something similar to Texas holey rock, and lava rock. I have never seen the traditional Japanese iwagumi stones in San Diego.