Near the entrance area of Dragonspine mountain, there is an area with Ancient Carvings. Light up the unlit torches surrounding it, and an enemy will approach. Defeating it will reveal a treasure chest, and you can interact with the lit Ancient Carvings safely. This is part of a "side quest" where you can obtain a free 4 star claymore: "Snow-Tombed Starsilver".
The Great Snowboar King
To the east of the teleport waypoint shown in the image above, go to the place marked with a monster icon. There you will see some ice tombs, where a snow boars are frozen. Melt the ice with Pyro attacks and kill all the boars to reveal a secret boss: "The Great Snowboar King".
At the edge of the island on the bottom right of Dragonspine, there is a drifting bottle that you can pick up. It's right in front of the Ruin Grader. Picking it up will give you some Mora and 30 Primogems.
Crimson Agate Luxurious Chest
On the small island just below Dadaupa Gorge, there is an ice that can only be melted by using a scarlet quartz. Go to the lower edge of Dadaupa Gorge shown above, pick up the scarlet quartz, and shoot the ice down using any archer character.
Warming seelie near lake
At the lowest level of the marked area shown above, near the lake, there are sealed pillars with a warming seelie that starts in the middle. Surrounding the pillars are unlit torches. The warming seelie will go towards the torches if you light them up using a Pyro attack.
To solve this puzzle, you simply need to guide the seelie by making it touch the unlit ruin braziers near the cryo pillar close to the middle.
There is a hidden unlit torch close to one of the broken boats that you need to reveal as well, in order to complete it.
8 Circle Rings
In the western part of Dragonspine, you can find 8 circle rings in the marked area shown above. The solution to the puzzle is:
From the Statue of the Seven in Dragonspine, melt the ice that's shown above, using the scarlet quartz that's available on the other side of the circle from the Statue of the Seven. Then activate the device to turn on the wind upcurrent in the middle of the circle.
Riding the wind upwards, you can see some devices embedded in the pillars. There are 3 in the circle of pillars. Activating them all will reveal some treasure chests.
In the spot marked on the map, when you try to climb the tall mountain, you can see some blue seeds sticking on the sides of the mountain. Get close to it so it will trigger. Detonate all of them to reveal a hidden chest.
As you start to go down the mountain, there is a small blue crystal that you can touch. It starts at around the marked area shown above. Touching it will make the next one appear, and it will guide you all the way down to the end, where there will be a treasure chest that appears if you complete it properly.
Non-quest related arena
In the marked area shown above, there is a small arena-like area, with a time trial challenge device in the middle. Do the challenge to fight some enemies, and get 3 treasure chests as a reward, including 1 with a crimson agate.
Find out what happened to one of the long-lost investigation team to where they embarked on their journey home by following the Ragged Records. At the end of the trail, you will get an achievement, as well as a crimson agate treasure chest that requires feeding some foxes.
Futile Endeavor Achievement
Interact with all of the broken ruin guards that gives you a message to get the achievement "Futile Endeavor" for 5 Primogems!
Buried treasure chest
In one of the small islands on the southeast area, there is a place where you can dig to get a treasure chest.
Other dig spots (wooden planks)
Near the end of the journey to unlock the peak of Vindagnyr (Hydro&Cryo domain), you have to climb all the way up the mountain. There are some treasures that you can dig that's shown with a wooden notice board.
Some (or all) of the wooden planks disappear once you pick up the treasure. So if you don't see it, maybe you have already picked them up.
The first location is close to the top of the mountain, near the last Anemo pillar that you need to activate to reach the floating pillar. There is a wooden plank near an unlit torch. Approach the wooden plank and "dig" for the treasure.
Second treasure spot with a wooden plank is in an obscure location. Head to the place shown above, and try to find the one with a dead tree. It's still somewhat near the top of the mountain. Once you find the dead tree, the wooden plank is just on the other side.
Third location is inside Starglow Cavern. Start by going to the teleport waypoint shown above, and head into the cave.
In the cave, you can find a hilichurl, not far from the entrance, that's busy trying to dig for something. Go to the spot and take the treasure.
Fourth treasure spot that you can dig is also from the same teleport waypoint. Turn around, and before going down into the circle area to go into the cave, go to the small crevice right beside it, close to the dead trees.
Fifth location is near the colosseum-like area in the outskirts. Climb up to reach the location shown above, until you see a wall with an unlit torch. The wooden plank is just on the other side of the wall.