What are some ways to find and purify water if you're stuck without water in a zombie outbreak? Lack of water, having no water to drink, or drinking tainted water that causes you to get sick is as dangerous, if not more dangerous, than encountering zombies.
If you're in an urban environment, a great place to find water that people don't think of is hot water heaters. Every building that has water needs a hot water heater. As long as it's not tankless, you're looking at plentiful amounts of water for you to drink. All you need to do is purify it ahead of time, and it's good to go, sitting there for you. Another place to find water if you're in an urban environment is golf courses, cemeteries, parks, any place that will have water features that aren't regularly used for purpose of drinking.
If you haven't prepared ahead of time with water purification tablets, and there are a whole range of them you can find, one way to purify water is by using common household bleach. You can add 1 part to 50 of bleach-to-water, let it sit for about 20 minutes. After that, it gives you that little bit of bleach smell, you're good to go. Kills all the bacteria in the water and you can drink it.
If you don't have any way to measure out the bleach while you're adding it to your tainted water, a good rule of thumb is add enough until you just get that faint smell of bleach. Let it sit for about a half an hour, then it's good to drink. It's the same concept as a swimming pool, the chlorine that cleanses a swimming pool, and that is another great place to find water if you're trapped in a urban environment. Look for swimming pools, you can drink that water.