All newer ships have an on board water purification system (potable water). The water is perfectly safe, on the ship. In port, either fill a bottle on the ship to take with you, or buy a bottle of water. Best wishes and have a wonderful cruise!
Actually, the ships are "making" fresh water from sea water and I would even go so far as to say it (the fresh water) is probably safer than what we drink in most of our US cities. (According to a post by Dave56, he used to do this when he was in the US Navy).