On The Moon In The Technic History

In 2057
There is an "Apollo University Communications" in Leyburg on Luna.

In The Twenty Fifth Century
Elfland, Lunograd, is "...a giant bubble of air..." (David Falkayn: Star Trader, p. 333) enclosed in an electromagnetic screen on the Lunar surface.

In Lunograd:

many corridors, including Gagarin, end at Titov Circus, an excavated cylinder with a domed skylight, showing Earth and stars, and thronged encircling balconies where Ivarsen Gems, the Martian Chop House and Serendipity Inc. do business;

a large sports goods store sells vac suits and vehicles and also collapsible boats with gaudy sails for low-weight sailing on the small Lake Leshy;

people float down dropshafts on gee-beams;

on many sublevels, wide, high, grime- and oil-overlaid corridors are crowded with freightways, robotic machines and pedestrians in work coveralls;

there are factories, warehouses, shipping depots and offices and odors of humanity, chemicals and electrical discharges;

hot gusts come from fenced grilles;

the constant vibration of the great engines is deep and almost subliminal;

the Hotel Universe will pay one million Commonwealth credits to any oxygen-breather whom it cannot accommodate and has twice spent more than a million, once to synthesize dietary requirements and once "...to fetch a symbiotic organism from the visitor's home planet." (p. 360)

Selenopolis is in Copernicus.

The capital of the Lunar Federation is, like Lunograd, in Plato.

In The Thirty First Or Thirty Second Century (see here)
Dominic Flandry must spend two weeks in Luna Prime after returning from a mission.