According to the book Bruce
by Peter Carlin, around 1970 Springsteen took his girlfriend out to a family meeting at his grandfather Zerelli's house, which they referred to as "the house on the hill."
The lyrics in the song also mention a sister, which suggests Bruce implicitly talks about his sister. Later in the book there is a confirmation of this: "Recollections of a summertime party in "Mansion on the Hill" (the name clearly reminiscent of Anthony Zerilli's House on the Hill) filter through the stalks of corn where the uninvited young narrator hides with his sister to take in the music and lights."
Rasmus - Stockholm, Sweden, for above 2