Accessing the two treasure chests that are under the villa?
Solution 1:
I think that those two are located under the front door pavement. You can get there via the well that is located on the left when you exit the villa from the front door.
DMA57361 provides images itself (from comms):
Going to the well:
The puzzle to the chest
And there you are
Solution 2:
These are in the mine. This area is accessed from outside the town, at the base of the hillside just behind the villa - the entrance is obvious, but sealed. You'll unlock it once you make that upgrade to the town.