Historia Antiqua Chapter: Act I - Sal Flore
Zhongli's Story Quest
Monoceros Caeli Chapter: Act I - Mighty Cyclops' Adventure!
Tartaglia/Childe's Story Quest
Note that under normal circumstances, Ganyu's Story Quest would come next. However, it is fine to delay, and we can't play it now anyways because of the interlude that we're still avoiding
Alatus Chapter: Act I - Butterfly's Dream
Xiao's Story Quest
The World Quest Hereafter unlocks the next day near Wanmin Restaurant and acts as an epilogue. Feel free to play this quest now or after Lantern Rite if you wish
Papilio Charontis Chapter: Act I - Yet the Butterfly Flutters Away
Hu Tao's Story Quest
Event: Lantern Rite
Version 1.3 Flagship Event
Lantern Rite is a yearly event in this game, and there's been a new story every year associated with it. As a Chinese game, Lantern Rite lines up pretty closely to the Lunar New Year, and it's always exciting to see the festivities
This Lantern Rite acts as a continuation to Xiao's Story Quest
Hangout - Chongyun: Act I - Signs of Evil
Chapter I: Act IV Prelude - Bough Keeper: Dainsleif
You can finally talk to Mondstadt Katheryne again to start this quest. Although labeled as a World Quest, this Quest is essentially an Archon Quest and is absolutely necessary to progress the story later
Event: Invitation of Windblume
Version 1.4 Flagship Event
This event introduces a Mondstadt festival: the Windblume Festival. This is also a recurring event, although not as frequent as Lantern Rite, but still worth watching for sure
Hangout - Barbara: Act I - Wellspring of Healing
Chapter I: Act IV - We Will Be Reunited
After two nation arcs, this quest finally focuses back on the Traveler's story arc. Despite it being labeled as such, it is not really a Liyue Archon Quest, just an Archon Quest
After completing this quest, avoid the teleport waypoint overlooking Liyue Harbor until it's time for the next Archon Quest