Arcane Eggs are by far the rarest and most valuable relic found in Hollow Knight. The item can be found in 4 different places and sold for 1200 Geo each. Combining this all together will give you a total of 4800 Geo for all of them.
Arcane Eggs – All 4 Locations
Here is a compiled list of all 4 locations:
1. Located below the room where Lifeblood Core is found.
2. Directly west of where Shade Cloak is acquired.
3. In the south part of Birthplace.
4. Given by the Seer in the Resting Grounds as a reward for 1,200 Essence.