I can answer the "when" for you (with the help of Harvey Fuller)...

The downtown Barbary Coast was located at 202 S. 1st Street, and was only open from 3-1-66 thru 5-3-66...according to Fuller's Index.

Previously that address was the location of the Hotel Elwell, from 1-9-51 thru 9-16-65. I could be wrong, but I seem to recall that there was a furniture store in part of the building while the Elwell was open...though I don't think the furniture store was there the whole time that the Elwell was.

Currently, that's the site of the Golden Nugget parking garage.