Since I suffer from sleep apnea, the first stop is always a long quest to buy distilled water for the humidifier of my device. I wound up buying this 1000ml bottle of sterile water in Pattaya at a Pharmacy called Fascino. It was about 53 baht. It is called sterile water here instead of distilled water.
They did not have it, at least in Pattaya or Bangkok, at the more available spots like Boots. Sometimes though asking at a full service pharmacy they can point you in the right direction. On Khao San Road one small pharmacy took the time to write out directions to a pharmacy supply that was afilliated with a nearby hospital.
Some in the forums suggested it might also be available in auto supply shops as it is used in motorcycle batteries.
Good luck.