Go to this page and have a look! (I tried embedding the video here, but it doesn't play satisfactorily at all at DSL speeds.)
The 6-minute film consists of three clips. In the first two, the car with the camera drives west up Second Street starting just west of Olive, then turns south on Grand. In the second clip, the car turns west from Grand onto Fifth Street and drives past the Central Library. The third clip starts just north of Fifth and Flower, proceeds up Flower to First, and ends just as the camera car crests the very top of Bunker Hill.
I think I can date this film pretty precisely to Summer, 1948. Just north of Fifth and Flower is a billboard for RCA Victor televisions that depicts a cartoon donkey and elephant wearing boxing gloves, with a caption saying "Pick a sure winner!" This suggests to me that this is a post-war national election year, with the national party conventions soon to be broadcast (these have always taken place in mid-summer). The style of television depicted on the billboard also looks post-war.
Then, just as the car turns east on First, another billboard advertises a show at the Hollywood Bowl running from July 25-Sept 5; another clue that this is summertime. Also, several of the cars in the film are post-WWII models. Although I'm no real expert on the subject, I don't see any autos here that date later than the 1948-49 model year.
Anyway, I highly recommend downloading the hi-resolution 217.8 MB MPEG4 file on the Archive.org webpage. The size and detail of the image is amazing. It really brings Bunker Hill back to life!