I give mine unfiltered tap water. That way they get trace minerals they may otherwise not get.
You'll find there is no clearcut answer on where to feed and water. Some of the things I'd consider.
If you feed them in the coop, you might wind up feeding fewer wild birds, thus saving feed.
If you feed them in the coop, they will spend more time in the coop, thus increasing the amount of poop you need to "manage".
If you feed them in the coop, the spilled feed could attract mice and rats. It will in the run also, but most people can handle them out there better than in the coop.
If you lock them up at night, I think they do need access to water when they wake up unless you let them out as soon as the sun comes up. I don't think having feed in there for them is as important.
How often are they confined to the coop? Do you have weather they cannot go out to eat and drink?
They need access to water all the time they are awake. I find if it is in the run and they are free ranging, they will go back to the run to get it when they need it.
If you have a really hot climate, I'd be a lot more inclined to give them easier access to water. For most of us, I don't think this is a consideration, but in some climates it could be important.
Wherever you put the water or feed will cause them to hang out there more, thus increasing the poop in that area. Maybe you want to fertilize certain areas?
Hope this helps and hope others chime in with other considerations.