They mention California several times, so it must have been NBC Burbank (which had opened specifically as a color studio in 1955).
https://en.wikipedia.org/wiki/The_Bu...tudios_Burbank
The camera alignments did not strike me as up to the usual NBC west coast standards, but part of that impression may be due to the overly strong color in this transfer to mpeg.
Crosby and Martin do a great job of carrying the program.
The production and scenery is very simple, which could be OK, but is cheap looking when you see the marks on the floor.