Starting in Mondstadt, go north of Stormbearer Mountains, past the Anemo Hypostasis boss, and go to the waterfall area. Drop down to where the waterfall is, and you will find a luxurious chest.
Side Quest - Time and the Wind
This area is related to "Time and the Wind" side quest. It's located at the secret island east of Starsnatch Cliff. Near the sundial that's at the center of the area, drop down into the water and you will find a small little opening that has a luxurious chest.
In the city of Mondstadt, there are 3 Luxurious chests. The first one is very close to the teleport waypoint that's on the roof of the Favonius knights building. You can see the Luxurious chest just to the side.
In front of the Cathedral
The second Luxurious is in front of the church. Go near the stairs that leads up to the church, and get close to the railings. You will see a small light when you get there. Climb up and there will be some light rings to guide you to where you should go.
Above the Cathedral
The third one is at the top of the church building, all the way in the back.
Side Quest - Break the Cemetery Sword
This Luxurious chest is from the quest "Break the Sword Cemetery Seal".