By the time of The Walking Dead, just like Los Angeles, it is hinted San Diego was engulfed in chaos and destruction during the outbreak and therefore became overrun by the dead. San Diego was declared overrun and as a result, completely burnt down, in accordance with the regulations of Operation Cobalt. It is possible a few survivors managed to escape San Diego, considering Travis' group stumbled upon the remains of a destroyed boat with logs stating the city of San Diego was completely burnt.
By the end of Season 1 of Fear, it is strongly hinted by survivors like Castro or Richards that the city may have survived and have elements of the California Army National Guard in operation, as they were heading to the city. However, it's unknown if this was true.
The ship log that Nick picked up from the overturned ship reveals that San Diego has been destroyed by the military. Although Strand is skeptical of this information, it is confirmed by George Geary, who states that the military napalm bombed the city just as they did to all the cities along the west coast and as far as the continental divide. He based this statement on his radio conversations with other survivors.
However, this assumption is thrown into doubt when Brandon Luke and his group state that they are heading to San Diego and that it hasn't been touched by the military bombardment, although given the fact that Brandon's group was in Baja California during the inital outbreak it's possible that they don't know the full extent of the apocalypse and its aftermath in the US.