You can always get a free cup of ice water from any drink location if you ask. That tastes better than the water fountains.

I've used one of those Britta filter bottles at lot at the Disney parks. It helps, but it's bulky and I can't just toss it away.

Now I like to carry bottled water into the park (never any question at the gate) so I can toss the drink when I'm done. Sometimes I refill an empty bottle from a water fountain or pour my leftover super-size softdrink into an empty bottle.

If you're staying on-property, those refill mugs at the resort are a pain. Yes, you can get free refills at the resort, but you end up hiking back and forth to the food court way too often and end up packing empty mugs at the parks all day long. In the end, it's easier and cheaper to buy bottled drinks. Eespecially if you bring them or buy them off-property.

We usually pack a suitcase full of bottled drinks and kid snacks like mini-doughnuts. That way we have an empty suitcase for purchases, etc.