This is the Third Street tunnel at the west entrance with Hope Street above.  In  the clip below Zachary Scott and Steven Geray drive through the tunnel and turn onto the Hope Street frontage and go into the Hotel Elmar which is visible on the left corner above.

The Third St tunnel at the Hill St entrance with Angels Flight above.  The funicular stops at the top on Olive St.

Looking south on Hope St, above the Hotel Elmar.  The stairs lead to the front of the hotel.

Hope St looking north with the Elmar at lower left.

Scott and Geray inside the The Elmar.  The hotel  was used for interior shots.

The Unfaithful  (1947) with Zachary Scott and Ann Sheridan was another film shot  in Bunker Hill.

Glenn Ford and Ricardo Montalban on stakeout in the 1966 noir The Money Trap.  This was one of the very last film noirs to be made.  The house they are surveilling is the Brousseau Mansion at 238 S. Bunker Hill Ave.  By this time redevelopment had cleared most of Bunker Hill and this was one of the few remaining old houses.

The Brousseau Mansion had been built in 1878 by the family of the same name.  By the 1940s it had been converted to a rooming house and was torn down shortly after filming of  The Money Trap.

This clip from The Unfaithful shows how the hotel scene is played out as Zachary Scott and Steven Geray drive to the Hotel Elmar on a foggy morning.