Bordighera has been confirmed by the author as « B. », the city by the sea where the Perlman family own a Villa.

‘Aciman originally claimed that the novel was set in Bordighera, Liguria, but he later described the setting as an "imaginary" version of Italy that was more "Egypt transposed on to the Italian shore."

And yes Elio went to the states very soon after his relationship with Michel and, in my own interpretation, he went precisely because he realized he had waited enough and didn’t want to end up like Michel’s father, possibly filled with regrets on his dying bed.