Sadly, I can't take any credit for locating the following location because the background was given to me by a very helpful chap by the name of Ventsislav Doychev (https://twitter.com/VenDoychev). To cut a long story short I had offered to find out where Club Obi Wan was and failed miserably, only to have Ven come back to me a few months later with all the information on a platter. So a big thanks to Ven for letting me know.
The opening scenes in Temple of Doom involve Indiana Jones (Harrison Ford) trying to do a deal with the evil Lao Che (the awesome Roy Chiao) at Club Obi Wan in Shanghai. Jones gets poisoned for his troubles and then shot at before jumping out of the window of the club and making off in a car whilst being chased by the baddies.
The good news was that the location has been identified (by Ven), the bad news is that building used for Club Obi Wan has gone. The only clue was an old photograph - purportedly taken by one of the production crew when they were doing a location scout - that shows the building concerned (I have no idea whose photo it is so if you know please comment so I can correctly attribute).
The green building at the back was the one converted into Club Obi Wan for the purpose of filming. It may not be too obvious from that photo but some closer inspection of the screen captures reveal the same windows, balcony railings and green colour of the walls. So, what and where was it?
The building was actually a hotel called the Pensão Sun Sun Hotel and it was located near to the inner harbour along Praca De Ponte E Horte. Can you see the building in the foreground? It didn't look so great back in 1984 when the film was made/released, but following the Macau Govt's sprucing up of old buildings it now looks pretty nice. Below is the recent Streetview taken at the best angle I can get to match.
As you can see the Pensão Sun Sun Hotel has been replaced by another building. It's still a hotel on the site but now it's the Best Western Sun Sun Hotel.
So anyway, here are some of the screencaps.
These shots shows the chaps (actually it was Vic Armstrong and his wife Wendy Leech doing the stunts in place of Harrison Ford and Kate Capshaw) falling down the side of the building and through some awnings before catching hold on to a building on the opposite side of the road (in this case it was the slimline Rua Do Bocage next to the hotel).
Now, sadly, the row of balconies you can see in the background of the above screenshots has also disappeared, however, it does appear that the stunt was done so that they landed on an awning sticking out from the nice yellow building that is still around. Here is a modern Streetview of Rua Do Bocage.