On the Grand/Caribbean Princess ships, there is a table near the exit door that will have water and canned soda. If you have a medallion, they will scan it. If you have Plus or Premier, it won't cost you anything and doesn't count against your 15 alcoholic drinks. Often the water is chilled.
For the sake of convenience, I find it easier to grab a bottle from the bar the night before. Then when I am preparing for the day, I include the water in my carry off bag. Otherwise, you are struggling with your medallion, crowds of people, and no hands free.