The Mythic Stones can be found on any floor below the 60, however the floors 60,102,152,155,171,190,202 and 222 you can find Jewel of the Harvest Goddess, which joining the 9 that can be found on the floors mentioned, form the Gem of Harvest Goddess, a tool whose function is to restore your stamina and fatigue whenever you want. They will randomly generate after having all of your cursed tools blessed. They will not appear until your cursed tools have been blessed.
If you manage to find a Mystic Stone, you can bring it to Saibara and he will upgrade your tools to the final level. Your blessed tools can be upgraded to Mythic Tools, which is the 7th and final level of tool. It will cost you 50,000G and two days duration for each tool you wish to upgrade.