The stereotype of medieval Europe is that people only drink alcohol because that’s their only sanitary option. I’m no historian, but I’m reasonably sure that this is exaggerated based on my classmate’s response to a beer-only diet.
Rivers seem like the obvious source, but not every human lived near one. What are alternative sources that people used? I can’t imagine that wells were that easy to install, and certain climates seem like they’d be less than permissible of the practice.
Water was not the preferred option in medieval western Europe, but yes, people absolutely drank it. In some towns, rivers were indeed one source, but other rivers were known to be polluted and unsafe to drink--unless, of course, you boiled the water first. Which, yes, medieval people understood. There's a fourteenth-century text that purports to be a letter from a Valencia man to his sons at university in Toulouse that instructs them to "cook" the water they get from a couple of nearby rivers because it's known to be dirty! (The "letter" is more likely a booklet that circulated as an advice book for new-ish students at the university than an actual letter sent by a father).
On farmland or in less settled towns, creeks and irrigation ditches could be used for washing clothes, fetching drinking water, and so forth. Coroners' reports (accident investigations) from late medieval England include cases of toddlers who drowned while trying to fill a cup with water, for example. In the hagiography (saint's biography) of Elisabeth Achler in early 15th century Germany, the other sisters at her monastery get cranky about how often they have to haul laundry down to the creek because her stigmata are bleeding and ruining her habit and sheets every day.
In the hagiography, their burden is relieved not by God turning Achler's stigmata into spiritual ones rather than physical, so the sisters can not have to do work...but by Achler miraculously pointing to a place in the convent courtyard where they can dig for a wellspring. And ta-da! They have a well, and they can do her laundry every day right there.
As the above reference to irrigation ditches suggests, medieval people were actually quite skilled at water engineering. (After all, they figured out how to drain and keep-drained the Low Countries!) Combine that with the locating and use of wellsprings, and you have the bases for an urban water system of fountains and drainage! In Italy, there are even cases of towns that pumped their water up a hill slope from the river or springs at the bottom to the town located above. Large fountains were important not just because people needed water to drink (and, one remembers, to make beer and ale in the first place!), but also to fight one of the biggest hazards of medieval life--fires.
None of these are revolutionary or surprising sources of water, in general. We just need to have a little more faith in medieval people.