Cultural spaces are tricky to explain. You can imagine that some creatures would have many communication-community style chambers and many would have none. Elves, for example (even the drow) would have all of these cultural rooms and more. Giants would have ancient traditions going back as long as their rivals, dragons. Celestials would encourage mortal events and be there to see it happen.
Contrast that with less culturally focused creatures.
Oozes would have nothing to say, do or even think. Aberrations could easily have too much chaos - gibbering mouthers wouldn't even tend to gather. You, as the DM, will want to work with this. Oozes, used or owned by a black dragon, may well end up as tools for some event. Aberrations with intelligence may have 'surreal art & sculpture' or even 'worship of the Unknown Gods'.
Depending on your monster you may want to include twenty more of these space-concepts or none. That said, please give it a try. You may end up with one of the examples at the bottom.
Basic Cultural, Sport, Religious &/or Entertainment Rooms:
- Religious festival: religion itself is covered in safety & sanctum. Religious events, however, involve public display to non-believers & quasi-believers.
- Music & Movement: dance, music, play, movie, theatre, animation-projection
- library, printing press, simple art
- sculpture, murals, mosaics
- festivals, parades, parties, celebrations, time o' year, carnivals
- travel, diplomacy, spelunking,
- swimming, skiing, jogging, gymnastics, sails on water or in the air (para-gliding or -sailing)
- odd device interest: kites, go carts, fireworks, sand sculpture
- collection: ogres = skulls, dragons = treasure ('amazing ancient coin collection!'), stone giants = amazing portable stone carving, wizards = weird low-magic items, fighters = war gear (swords, knives, helmets),
- Magical Cultural Function: based on one spell that moves beyond a usual scope - see below.
Magical cultural function can include the (ab)use of any spell, monster or magic item:
- making wines out of Goodberry juice.
- a permanent Zone Of Truth that youth use together as a hazing ritual / rite of passage / means of building relationships.
- a DreamZone: all who sleep in this chamber can partially control and even share dreams.
- laboratories where cheap potions are mixed to gain dangerous results
- a medusa that makes a killing off of selling both her victims and basilisk-bile processed by alchemists.
- a green dragon's elf conversion chambers
- ancient wizard's clones & simulacra that were used in weird experiments
- all sorts of abuse of 'Fabricate' by any wizard artisan (a half-thousand year old elf may have more than a hundred thousand works laying about!)
- Quidditch-style sports: on brooms or carpets, boots of spring-jump, slippers & gloves of climb-sticking, levitation-style 3D sport-courts and much more
Specific Races & Strange Examples Of Culture:
- Goblin mosh pit: hard rock music and the weird alcoholic beverages taste surprisingly good once you muscle through the first three.
- Orc Of Sport: why must this race outsource all of their pent up energy? Why not save the best of their activities for their own players?
- Religious Illithid: alien minds each slowly devouring priest and cultist brains - sharing this concept of a sentient creature giving everything they have to a being that they will never meet never meet.
- Sculpturing blind duergar dwarf: (super)natural-magical stone shaper works for a medusa - can somehow shape petrified creatures without damaging them and can add physical abilities & occasionally a few charisma points. Also can put them in new positions and even add stone to give them different outfits.
- Mindful Mimics: they may share or compete for different shapes, textures, sculpture forms or any number of other things.
- SpellBreaker Competitions: wizards of different guilds or schools could compete for spells &/or magical items of most original, most useful, most powerful or whatever other categories.
- Dragon Weird: dragons of adult age may discuss boundaries in order to prevent or avoid dragon slayers from becoming a problem, rivalries from killing off entire lines of drakes, etc.
- Teleportation chambers: some would have the rune-formulae marked on pillars, walls, nearby floors or archways.
- Incineration / Disintegration Tubes: Beholders leave long, insane and yet surprisingly logical tunnels.
- Fiend Binder Room: Evil spell casters (especially Drow) love to summon &/or bind extra-planar creatures. This room would help.
- SpiderWeaver: Spider silk is five times stronger than steel. Imagine what giant spiders could weave with their 4-7 kinds of silk! Or what phase spiders could weave.
- Fae celebrations: What is a massive yet tiny party like?
- Ogre gambling & drinking room: the furniture, made of ironbound stone, would still probably be badly damaged.
- Troll Harvest Room: Someone is eating the troll! Again.
- Giant Rock Tossers: The name says it all. Competition invites many ordinates and the Rock guys tend to win. Rock Giants also play rock music. Event held at the same set of massive rooms every year that include both icecold and lavahot spaces.
- Archdruids make a magical version of StoneHenge that is many times bigger - and with much better sculptural shapes than 'brick'. With nifty rune-lines carved in. That glow. Just better!
- Elder Brain is smart enough to predict a Gith-raid (one or both kinds). Has built a transport room-building-device complete with servants, guards & food-brain 'friends'
- Treants gather at a moot-place. The trees around them are ancient and enchanted, making it a set of a few massive living-wooden rooms.