Returning to this card I posted last year:
I think you're right about it looking east on Bancroft, but you wouldn't be able to see the Campanile from this angle; it would be too far off to the left. The building visible beyond the greenery looks vaguely like International House (which opened in 1930), and that's where it would be in relation to this intersection.
It turns out that I was wrong. Yesterday I saw a large photograph of this intersection from roughly the same time, and the street sign on the cross-street (by The Owl Drug) says BANCROFT. So the postcard has us on Telegraph, looking north toward the campus, with Sather Gate down at the end of it, hardly visible, and Wheeler Hall beyond that (yellowish in the picture). The Campanile is hidden from view by the tall buildings on the northeast corner of the intersection.