I ... will just throw in some ideas here...
I think there shouldnt be more than 2 choices for each slot to prevent cluttering and the choices should at least roughly be in line with what the district stands for, but may allow leaning towards other district types.
Theatre square:
Amphitheatre - Opera house: The opera house would unlock much later (renaissance), but has space for great works of music and yields great musician points way earlier than you could put up broadcast centres.
(Museums)
Broadcast Centre - Movie Theatre: The movie theatre has no slot for great works, but increases amenities for its city.
Campus:
Library - Academy: The library loses a bit of science, but gains one slot of great works of literature and maybe one writer point. The academy is focused on its science yield (basically, the former library).
University - Observatory: The observatory has smaller science yields than the university, but doubles the mountain adjacenty bonus.
Research lab - Botanical Garden: Less science than the research lab, but amenities, culture, and doubled rainforest adjacenty bonus.
Holy Site:
Shrine - Sacred Grove: The sacred grove forgoes the great prophet points and faith of the shrine, but yields doubled(?) pantheon yields in its city.
Temple - Monastic School: The monastic school yields less faith and loses the ability to create apostles, but offers science and scientist points in return.
Encampment:
(Barracks/Stable)
Armory - Keep: Instead of boosting the production/xp of units, the keep offers more housing and increases the defense strength of the encampment, allowing it to shoot even if its city has no walls (unlocked at castles).
Military Academy - Runway: Unlocked with flight, the runway offers the ability to station a small amount of aircraft in this encampment.
Commercial district:
Market - Caravansary: Less raw gold output, but trade routes originating from or passing through this city's trading post have longer range and increased gold return.
Bank - Guild Hall: Unlocked at guilds (duh), this building offers a fair amount of production instead of some of the bank's gold yield and adds production to incoming trade routes.
Stock exchange - Supermarket: Less gold, but additional food (including trade routes).
Entertainment district:
Arena - Fairground: Small amount of faith instead of the amenities. (The arena is so weak, it's hard to find a just as weak counterpart
)
Zoo - Garden: No regional amenity, but increased great people points for the city and a small amount of faith.
Stadium - Amusement Park: Only one regional amenity, gold instead.
Industrial zone:
Workshop - Forge: Military units are produced faster in this city.
Factory - Ironworks: No production by itself (and thus also no regional bonus), but adjacent mines have additional production.
Power Plant - Chemical Plant: No regional production bonus, and less local production, but science instead.
Harbour:
Lighthouse - Trading port: No food or housing, but more gold. (Note: I can't imagine a harbour without a lighthouse though. How about making the lighthouse graphic baseline to this building and renaming the lighthouse "Fishery port"
)
Shipyard - Bullwark: Unlocked at Castles, this alternative building has no further yields, but adds defenses towards the sea (protecting ships on the tile) and the ability to shoot (on water tiles).
Seaport - Deepsea Mining Base: Very late game building, that increases local production and the production of space projects for all of your cities. (This is a bit experimental, especially as there is a policy card that does basically the same locally. It allows non-spaceport cities to contribute though. Other ideas were around nautical research buildings.)
Aerodrome:
Hangar - Hotel: Instead of allowing more aircrafts and production, this building improves the tourism generated in the city.
Airport - Military Airbase: I think the Airport should be a building increasing tourism and gold, while the Military Airbase takes the airports former production and aircraft bonuses.
