Anime shows also have Giant Monsters!
Giant monsters attacking cities is a pretty common science fiction or horror scenario in Japanese media. The reason being possibly that since people live pretty close together, the idea of a giant monster coming and wreaking havoc is particularly scary and destructive.
I know a certain Anime show called "Dai-Guard", which is a show about a decommissioned robot specifically designed to fight one monster that keeps coming back for more: Heterodyne!
This show is fairly humorous and often involves the giant robot "Dai-guard" not really functioning the way it should. But the threat of the monster is very real, and it's up to dai-guard and the rag-tag operating crew to put a stop to it once and for all.
Try watching Episode 1 here!