I---like to know where you were born.

我个人认为这不是虚拟语气。Where you were born 出生是指过去的瞬间动作,后面这句译为:你的出生地,并非虚拟。此处选用B should 是英语的一种常见形式, like与would,should 表示客气,委婉的一种语气,缩写形式:I'd like。 希望这样回答,你能明白。