Location Detective - Edie's Cocktail Lounge
The mansion and cemetery have been discussed, Edie's Cocktail Lounge was filmed at the specific address mentioned in the film - Figueroa & Temple, downtown. The tall building under construction in the background, is still there, as a landmark.
The building housing Edie's lounge is still there, but quite altered - you can identify it by the main door of the entire building, next to what was "Edie's" (now bricked up), as well as some of the masonry of the structure. Although the building is suggested to have a second story in the film, it actually never had one. You can view the location on Google StreetView from the exact same location seen in the film - it takes a little maneuvering.
It appears that were were several individual "garages" off Figueroa in this relatively small building, in the 60s, and that "Edie's" was one of them, with a fake facade. Obviously, the interiors were a set. Those garages are all now bricked up, with no windows.
Surrounding buildings have been replaced, except for the aforementioned tall building under construction during filming.
UPDATE: "Edie's" actually faces N. Figueroa Street, close to the corner of West Temple Street. It's hard to find on Streetview, because Figueroa briefly splits at this point, with an upper and lower level for a few blocks. The building is gray, with a large billboard above it. It is surrounded by empty lots - the only building to survive that downtown block since the 60s filming.