There is water available; however, I do not recall seeing any water fountains per se.
In the Windjammer eatery where you serve yourself, there is water right there in the buffet/drinks area where the cups, ice, iced-tea and lemonade fountains are.
In the main dining rooms the water is provided by your waiter---tap water on ice. There will be an ice bucket in your stateroom and the water out of the bathroom tap always seems just fine to me.
If you want water with you poolside, just help yourself from the (I'm pretty sure) 24-hour coffee/tea station.
I hope that this helps.