Here are some ideas and links to further reading:
CASTLES:
Council Chamber / Seat of Power: increased Diplomacy and Intrigue, increased opinion from Council members.
https://en.wikipedia.org/wiki/Great_Palace_of_Constantinople
Decorative Moats and Gardens: minor defensive bonus, increased Prestige, chance to gain Gardener trait.
https://en.wikipedia.org/wiki/Bodiam_Castle
Round Keep: large increased fort level, larger garrison, Martial bonus.
https://en.wikipedia.org/wiki/Château_de_Coucy or
Tower: prestige, moderate increased fort level.
https://en.wikipedia.org/wiki/Alcázar_of_Segovia or
https://en.wikipedia.org/wiki/Château_de_Vincennes
Epic Walls: large increased fort level, larger garrison, chance to gain Defender commander trait.
https://en.wikipedia.org/wiki/Castles_and_Town_Walls_of_King_Edward_in_Gwynedd or
https://en.wikipedia.org/wiki/Ávila,_Spain
Royal Hunting Grounds: increased chances of success during hunts, higher chance of White Stag event.
https://en.wikipedia.org/wiki/Jagdschloss or
https://en.wikipedia.org/wiki/Palace_of_Fontainebleau
Observatory: tech bonus, ties to Scholar.
Laboratory: tech bonus, ties to Scholar and Hermetic.
Drawbridge: increased Fort level, chance of gaining Strategist trait.
https://en.wikipedia.org/wiki/Citadel_of_Aleppo
Glacis: increased Fort level, chance of gaining Architect trait.
https://en.wikipedia.org/wiki/Krak_des_Chevaliers
MONASTERIES:
Library: +1 level for books composed by liege, increased Learning.
https://en.wikipedia.org/wiki/Abbey_of_Saint_Gall
Defensive Tower/Citadel: increased Martial, increased garrison size and fort level.
https://en.wikipedia.org/wiki/Convent_of_Christ_(Tomar) or
https://en.wikipedia.org/wiki/Stavronikita
Murals and Artwork: liege and clergy based here have high chance to gain Poet, increased Learning.
https://en.wikipedia.org/wiki/Saint_John_Abbey,_Müstair
Reliquary: allow liege to select an artifact, permanently attach it to the church, and create a minor Bloodline giving that bonus to the liege and his/her dynasty.
https://en.wikipedia.org/wiki/Vézelay_Abbey
Fountains: small Health bonus, small Disease Resistance, Clergy based here gain faster Piety.
https://en.wikipedia.org/wiki/Fountain#Medieval_fountains
CATHEDRALS / BASILICAS:
Belfries or Minarets: Piety, Prestige, increased conversion bonus for adjacent 1-2 counties.
https://en.wikipedia.org/wiki/Belfries_of_Belgium_and_France
Ornate Facade: Piety, chance to attract Architect or Master Builder.
https://en.wikipedia.org/wiki/Reims_Cathedral
Sculptures: Piety, resistance to heresy.
https://en.wikipedia.org/wiki/Reims_Cathedral
Stained Glass: Piety, chance to attract Bards.
https://en.wikipedia.org/wiki/Sainte-Chapelle
Altarpiece: Piety, chance to attract Holy Men.
https://en.wikipedia.org/wiki/St._Mary's_Basilica,_Kraków
Tomb of a Saint: if we have a Saint in the family, give us a chance to make him/her the focal point of the cathedral and increase piety further, and maybe increase the bonuses received from their bloodline by 50-100%.
Reliquary: (same effect as above in Monasteries) allow liege to select an artifact, permanently attach it to the church, and apply its bonus to all living lieges within a 1-2 province radius.
https://en.wikipedia.org/wiki/Shrine_of_the_Three_Kings
Baptistery: large increased Piety and Relations bonus for people baptized here, higher chance of attracting Master Builders.
https://en.wikipedia.org/wiki/Pisa_Baptistery or
https://en.wikipedia.org/wiki/Florence_Baptistery
TOWN SQUARE / TOWN HALL:
Administrative Hub: increase tax, decrease revolt risk, increased vassal opinion.
https://en.wikipedia.org/wiki/Kraków_Town_Hall
Clock Tower: tech bonus, small tax bonus.
https://en.wikipedia.org/wiki/Zytglogge or
https://en.wikipedia.org/wiki/Prague_astronomical_clock
Market Square: moderate to large tax increase, increased Burgher opinion, increased Stewardship.
https://en.wikipedia.org/wiki/Main_Square,_Kraków
Landmark Square: increased vassal opinion.
https://en.wikipedia.org/wiki/Grand_Place
Landmark/Symbolic Statue: prestige bonus, decreased revolt risk.
https://en.wikipedia.org/wiki/Holy_Trinity_Column,_Olomouc
or
https://en.wikipedia.org/wiki/Bremen_Roland
Jewish Quarter: increased wealth equivalent to a Trading Post, increased chance of Ashkenazi courtiers appearing, high chance of Sympathy for Judaism for liege and noble family members, small decrease to relations with Church, moderate increase to relations with Burghers.
https://en.wikipedia.org/wiki/Jewish_quarter_of_Toledo or
https://en.wikipedia.org/wiki/Kazimierz
PRE-EXISTING WONDERS:
For all existing wonders, a longtime owner (10+ years?) should be able to spend prestige and incur an opinion loss to destroy a structure and loot the stone for a long-term discount to construction costs within 1-2 counties.
Tower of London in London, England. William the Conqueror’s legendary structure is already on the CK2 map. Big bonus to Prestige, increase for Martial and Intrigue, reduced revolt risk, increased Plot Power.
https://en.wikipedia.org/wiki/Tower_of_London
Diocletian's Palace in Split, Croatia. Roman-era imperial retirement home. Upgrade/convert it into your own palace, mausoleum, or monastery for a choice of Piety or Prestige.
https://en.wikipedia.org/wiki/Diocletian's_Palace
Aachen Cathedral in Aachen, Germany. Burial place of Charlemagne. Liege can maybe kick out Charlie and use it for a big Prestige bonus at the expense of a negative relation modifier for Frankish descendants/culture, or instead maybe use it to bind their dynasty bind his and re-form his Bloodline.
https://en.wikipedia.org/wiki/Aachen_Cathedral
Mosque of Cordoba in Cordoba, Spain. Center of Andalus. Huge Piety bonus. Upgrade available as Muslim but also let a Christian King with high prestige do what happened later and convert it to a cathedral. Would increase Piety but decrease opinion heavily with Muslims and Andalus culture.
https://en.wikipedia.org/wiki/Mosque–Cathedral_of_Córdoba
Umayyad Mosque in Damascus, Syria. Center of religion in the Levant. Christian with high Prstige who owns it 10+ years should be able to re-dedicate it to John the Baptist for a huge relations malus to all neighboring Muslims but a huge relations bonus for Christians and a massive Piety bump. Mystic Muslim liege should be able to provoke the End of Days here.
https://en.wikipedia.org/wiki/Umayyad_Mosque
Zytglogge in Bern, Switzerland. Multipurpose 13th Century clocktower. Martial, Economic, and Culture tech bonus.
https://en.wikipedia.org/wiki/Zytglogge
Wawel Cathedral in Krakow, Poland. Focal point of Polish monarchy and coronation. Massive bonus for liege’s relations with Polish culture, increased chance of culture conversion to Polish among court members.
https://en.wikipedia.org/wiki/Wawel_Cathedral
Roskilde Cathedral in Roskilde, Denmark. Focal point of Danish monarchy. Bonus with Danish culture, Culture Tech bonus.
https://en.wikipedia.org/wiki/Roskilde_Cathedral
Thingvellir in Iceland. Focal point of Icelandic culture and site of parliament. Big relations bonus to all vassals in Duchy of Iceland, Culture tech bonus.
https://en.wikipedia.org/wiki/Þingvellir
Sherwood Forest in England. Give Robin Hood some extra events and make him either a true antagonist or eventually a trusted lieutenant depending on your traits. The forest itself could then either give you a tax and rebellion bonus, or a tax and rebellion penalty depending on your relations with the Merry Men. Even after Robin dies the forest can retain legendary status and either continue to be an economic boon or a curse for lieges. I suppose someone who wants a definitive end to the Merry Men could just burn down the forest and be done with it, though that should spawn a Bloodline with a permanent relations malus for all of the cultures in Britannia. (“Enemy of the Forest” or whatever.)
Acropolis in Athens, Greece. The Byzantines made a lot of upgrades and mods to it during their reign. Prestige bonus, Culture tech bonus, relations bonus with Greek culture.
https://en.wikipedia.org/wiki/Acropolis_of_Athens
Alhambra in Granada, Spain. Prestige, Sympathy with Christians/Muslims/Judaism for liege, Minor Health bonus (the water system and climate are great there!), probably a small Fort bonus.
https://en.wikipedia.org/wiki/Alhambra
Roman Walls of Lugo in Lugo, Spain. Fort bonus for all Castles and Cities in county.
https://en.wikipedia.org/wiki/Roman_walls_of_Lugo
Citadel of Aleppo. Increased Martial, Fort bonus for Castle, attracts Commanders.
https://en.wikipedia.org/wiki/Citadel_of_Aleppo
Carcassonne Fortress in Carcassonne, France. One of the few places to not endure Black Death. Effects for Hospital structures increased by 100%, additional Disease Resistance bonus, extra Fort level.
https://en.wikipedia.org/wiki/Cité_de_Carcassonne
Palmyra in Palmyra, Syria. Tech bonus for Culture, tax bonus equivalent to a Trading Post, small chance of liege to gain Architect trait.
https://en.wikipedia.org/wiki/Palmyra
Waterwheels in Hama, Syria. Waterwheels/aqueducts called Norias. Prosperity gained at increased rate within 1 county, minor bonus to Disease Resistance.
https://en.wikipedia.org/wiki/Hama
Petra in Petra, Jordan. Ancient Nabatean capital. Culture bonus for Levantine culture, tech bonus for Culture, small chance of liege to gain Architect trait.
https://en.wikipedia.org/wiki/Petra
Axum in Tigray, Ethiopia. Ancient site of Axum culture. Sympathy for Christians/Orthodox increased chance for liege and family based here, Culture tech bonus.
https://en.wikipedia.org/wiki/Axum
Lalibela Underground Churches in Lalibela, Ethiopia. Pilgrimage site for Miaphysite. High piety bonus, high same-religious bonus for Miaphysites, higher chance of Saint bloodline forming, non-Miaphysite owner has nigh chance of Sympathy for Miaphysite.
https://en.wikipedia.org/wiki/Lalibela
Meroe Pyramids near Shendi, Sudan. Whatever bonuses you decide to give to the Pyramids in Giza, give a version of those for this, too.
https://en.wikipedia.org/wiki/Meroë
SUPERNATURAL SITES YOU COULD DISCOVER / SITES LUNATICS COULD BUILD:
Atlantis. Maybe have a chance to discover it on the Canary Islands or the Balearic Islands if you have Superstitious events on, offer a big tech bonus I guess.
Tower of Babel. If you go insane or become a Mystic, start an event chain to try to succeed where they failed in the past. If you succeed maybe you have a shot to become Immortal? Not sure if it would be more appropriate to give piety, or take it away…
Monument to Glitterhoof/Dog/Cat. Obviously.