Poul Anderson’s excellent short story “Kyrie” has a convent of St. Martha of Bethany in the lunar mountains, where it has become traditional for those who have lost loved ones in space to offer up their prayers. Not exactly a “city”, but it’s certainly more than an “outpost or research station”.
In his 1962 short story “Searchlight,” Heinlein mentions Tycho Base, Meridian Station, Farside Hardbase and Station Newton. It’s unclear if they’re cities, as such, or just military bases (esp. the third). Does his The Rolling Stones and Have Spacesuit, Will Travel refer to others?
In addition to those named in the OP, Star Trek has also referred to Lunaport, the Lunar One colony and the Orpheus Mining Colony.
I’m currently reading Requiem For A Ruler Of Worlds by Brian Daley (I got the recommendation here on the SDMB), the first of a trilogy about the adventures of Alacrity Fitzhugh and Hobart Floyt. I’m not too far into it; the first stop on their journey is the Moon.
So far the list of cities/settlements/shanty towns named includes Lunaport (where their ship landed), Upsie (or This End Up City, the now-abandoned first “boxtown”), Hubble City and Sockwallet, a community of “foragers” or nomads.
One of my favorite MST3K-ed movie is “Moon Zero Two”, if just for the opening theme and the accompanying Joel Go-Go Dancing (actually, it’s not all that bad a movie - it has a reasonable plot and does hang together).
Wiki mentions the movies features Moon City (the main city where the shuttles land, and that cabaret is located), and Farside 5, which I believe is where the Monorail ends and where they rent the moon buggy to travel to the mining claims.
I believe the 1970 TV series UFO (1980) has (1980) only (1980) bases, not cities (1980)- the Shado (1980) moon base, and at least 2 other (1980) bases (the private mining base, and the Russian base where the run-away moon buggy-truck came from). Don’t recall any cities (1980*)…
(*I recently rewatched a number of episodes, and I believe during the pilot episode’s intro “1980” flashes on screen 4 times, while subsequent intros 1980 flashes only 3 time…so I guess we can blame former PM Margaret Thatcher for the lack of moon bases?)
I just checked in Heinlein’s Double Star, The Past Through Tomorrow and Have Space Suit, Will Travel. The first book mentions Tycho City, Jefferson Port and New Batavia (the capital of the Solar System-wide Empire). The short story “Gentlemen, Be Seated” in TPTT mentions the town of Richardson; “The Black Pits of Luna” mentions Rutherford. I counted seven TPTT short stories which refer to Luna City, as does HSSWT. That book also refers to Tombaugh Station, which might be a scientific outpost rather than a settlement.
There’s the Hurrian settlement, just called “the Base”, in Asimov’s “The Gentle Vultures.” It started out as an expedition base, but after 15 years was a settlement.
In Heinlein’s 1952 juvenile novel The Rolling Stones, Luna City is mentioned again, as is Leyport, probably named after this guy: Willy Ley - Wikipedia. No other lunar cities that I noticed in a quick skim of the book.
You may or may not want these. There is a board game called Lunar Rails, which involves building railroad from city to city on the moon. It has a plethora of cities, of 3 different sizes. You can see them in these 2 pictures, Far Side, Near Side. The round small ones are most likely mining or research stations, the square ones towns, and the 6 large ones major cities. Although in the game they are all called cities, just of different populations.
Although an English (ITC?) television production, SHADO was supposed to be an international agency in the series.
And here’s a bit of trivia, since you’re rewatching: Col. Virginia Lake is Bennedict Cumberbatch’s mother, and recently appeared as Mrs. Holmes’s mother in Series 3
of Sherlock.