Don't pay for water in Dubrovnik, you'd be wasting money and an opportunity to drink some great tasting natural spring water.
Bring a small water bottle and fill up as needed from the ornately carved fountains around town.
The grandest fountain, Velika Onofrijeva česma (The Large Onofrio's Fountain) is impossible to miss as you walk through the Vrata od Pila (Pile Gate). Mala Onofrijeva česma (Little Onofrio Fountain), (pictured and on map), is at the far other end of the Stradun.