As far I am aware, the first declared influence was on Bradbury's short story "The Fog Horn", the 1951 tale of a lighthouse destroyed by a lonely dinosaur. The story was the basis of the 1950s monster movie The Beast From 20,000 Fathoms. So where is the Venice influence? The dinosaur itself! In a frequently recounted anecdote, Bradbury tells how he saw the remains of the Venice Pier rollecrcoaster, and imagined it to be the skeletal remains of a dinosaur. Freewheeling from there, he asked what would lure such a creature to such a place. A lighthouse, of course!
But Venice has had more than one story's worth of influence on Bradbury. Much of the carnival imagery of his early stories is likely to have been influenced by the carnival-like Venice, California, which Bradbury probably first visited in the late 1930s when he was in his teens.
There are more images of Venice in its prime and in decline in the online photo collection of the Los Angeles Public library. Click here to see a selection.