I remember that, too, Jeff!
She and Carol had the best costume designer for their talents, Bob Mackie. He is even portrayed by an actor in The Cher Show. They've recreated a whole slew of his Cher creations for the show and during the production there's even a mini-fashion show segment!
It's amazing to think, but at one time The Carol Burnett Show, The Red Skelton Hour and The Smothers Brothers Comedy Hour were all taping at CBS Television City at the same time!
The Smothers Brothers got notoriously fired by CBS in Spring, 1969, and even though Red Skelton's show was still in the Top Ten in 1970, CBS cancelled it. (He then went to NBC for one more year in a half-hour version, but that didn't work so well.) So then in the summer of 1971 The Sonny & Cher Comedy Hour moved in while Carol Burnett was still there. Not to mention All in the Family, too, which began taping there in 1971. (After a few years All in the Family relocated to Metromedia Studios.)
Who can forget the beginning of some of those shows: "From Television City in Hollywood..."
Last December CBS sold Television City after 69 years! Read about it, here:
https://www.hollywoodreporter.com/news/cbs-sells-television-city-property-750-million-1168095And Metromedia, where all of Norman Lear's Shows ended up taping, was sold and bulldozed some time ago. It's now a large high school and where the sound stages were is a large track and football field. (Glee filmed many exteriors at the high school.)
I saw tapings of several shows at Metromedia from around 1977-80. I saw The Jefferson's, Three's Company (2), Apple Pie (3), Hello, Larry, and an All in the Family. If I saw anything else I'm not remembering it right now.