What about Sanford and Son? If memory serves, it took place pretty much entirely in the living room with short forays into the kitchen.
The wife was played by Barbara Barrie, a well known Broadway actress. A good bit of her in season one, then she did indeed vanish.
All of the shows mentioned so far sometimes visited other locations. The OP specified “locations that appeared all or nearly every episode”.
Peter Kay’s British sitcom “Car Share” takes place almost entirely within the car that John drives Kayleigh to work in. There’s an exception or two for the car park at the supermarket where they work, but even there they are getting in the car.
Wings was set almost entirely in the airport.
Somewhat similar was the Canadian show, Train 48.
It was a group of regular commuters heading home from work in the city, on a commuter train to the suburbs. And that was pretty much it: a soap opera that was told as the travellers discussed their day, current events, and the like.
Every episode, with one exception, took place in the train. The exception was the series finale, which took place mostly in the train, but did show the passengers getting off the train at the station at the end of the episode.
Untrue. They frequently showed the characters on dates, Chandler and Rachel’s various offices, sets where Joey was acting, etc.
Well, the OP didn’t exactly specify ‘sitcoms only’ - most quiz/game shows take place in a single studio.
All right, I’m going…
You beat me to it. 318 episodes in total!
I wouldn’t quite bet my life on it, but I’m almost positive that they only showed Barney’s house once, in the pilot episode. By the third season they almost never used a different set, only for the very rare ‘special’ episode (Wojo’s Girl, and the one where Barney goes to jail for contempt of court, and the one where Harris & Dietrich are staking out a hotel room). And, IMO, all those episodes were not very good (for that very reason).
They were part of the same set. At least once or twice I caught a glimpse of one of the other cameras just pulling out of the view of the live one. But it’s what made that show so good, it was simply a filmed (taped) three-act stage play…
Depends on your definition of almost. They frequently went to the Club Car, various houses owned by Helen, Joe, Brian, Roy, and Faye, also Lowell’s boat, the airplane in the air, the airplane in the water, Boston several times, somewhere out west taking the annoying old guy to visit his brother, scenes at a tropical resort somewhere, a romantic getaway cabin in the woods, a fish packing plant, a yacht, Helen’s apartment in New York and a strip club in New York, a bank, a hospital, a local men’s lodge, a courtroom, Fenway Park, a video store, the annoying guy’s house, a psychiatrist’s office, just to name a few.
But other than that it was set almost entirely in the airport. 
I think there were two episodes, the pilot and one other that took place at the Miller’s apartment.
Other than that there was a handful of other episodes that took us out of the precinct.
• In the episode where Chano is shot, there’s a scene with Chano in the hospital.
• During the overlap, when Fish was being phased out and Dietrich joined the precinct, a depressed Fish doesn’t come into work so Dietrich goes to Fish’s house to talk him into returning. This is the first time we see Fish’s house.
• Another episode is used as a back end pilot for the short lived “Fish” series. That episode takes place at the Fish home.
• Another episode has the cops go on a stakeout where they spend time at an apartment.
Really? Wow. Maybe I’m just remembering the opening titles where we see Barbara Barrie at the window.
I think probably most shows, other than police, fire, etc., have just a few regular locations. For example, the Dick van Dyke Show had just two–the Petries’ house, and Rob’s office. The Mary Tyler Moore Show also had just two–Mary’s apartment, and her office. All in the Family had only one, at first–later they expanded to three; the house, the house next door, and the bar.
Wasn’t Are You Being Served? mostly set in the store?
With the exceptions of scenes taking place in Mr. Rumbold or Mr. Grace’s offices, yeah, you’re probably right.
I believe NewsRadio took place only in the one radio station room.
Mostly. There were other locations. Jimmy James gave a talk somewhere based on the book he wrote.
Matthew was revealed to have always been a dentist and we saw his office. But who didn’t see that coming, amirite?
Aside from Barney Miller, you have WKRP in Cincinatti, Benson, Alf, The Paul Lynd Show, The Two of Us, Angie, Punky Brewster, Different Strokes.
Single setting format was an art back then.
I don’t know why people are still answering when this was the clear answer. If there was any show that had less different sets used than the Honeymooners, it’s something really obscure and lost to time.