Here is the photograph the postcard was evidently made from.
Note the return address of 625 S. Hope St.
This is what the 600 block of Hope looked like back then. Since odd numbered addresses are on the west sides of streets in L.A., 625 Hope must be one of those little cottages lined up between the Hotel Orena and Hotel Acacia.
Library of Congress.
A century later, that stretch of Hope looks just a tad bit different. ;) In fact, Wilshire Boulevard now cuts a wide swath right through where the cottages used to be.
And 625 S. Hope proper? Today, it's the site of one of Los Angeles's most familiar skyscrapers – none other than the United California Bank Tower (1970), which was the tallest building on the West Coast for much of the time I lived in the L.A. area.
Google Maps Street View.
Currently, of course, the UCB/First Interstate building is known as AON Center.