From "Rob Banzai" on Ars Technica reguarding "Cloverfield":
No one really likes blowing up L.A. because we have fewer landmarks. After you take out the Hollywood sign and Capitol Records you're pretty much done. "OMG HE'S GOING TO STEP ON THE BEVERLY CENTER!" just doesn't build much anxiety.
Plus the buildings are so short you'd see Godzilla coming from a looooong way away.
The big fella would probably get frustrated from having to stomp on three story buildings instead of rows of towering skyscrapers filled with hipsters.