Welcome to BYC and to the wonderful world of keeping chickens!
The answer is there is no one right or wrong answer to your question - as each person find what works best for them/their birds.....and for many folks, the exact plan you are considering is what they opt for. Things to consider in deciding where to keep the feed/water stations are:
size of your coop and run
the number of birds being housed
your overall climate
how well secured your coop/run will be (remember to consider times you might open the run to allow the flock to range, which defeats the "security" as far as other animals being drawn in to your enclosure to seek the feed/water if that is a concern you have)
whether you will be using electrically powered heat for the water in the winter and how easily accessible it will be to you either in or out of the coop
the ease of access to where you might put the feed/water stations - including on days when the weather might not be that nice or once the birds have been inhabiting the area for a while (this comes into play with keeping the feed/water inside a run that is too low to allow standing up inside or sometimes when they are kept under a raised coop, etc - you don't always think ahead to having to crawl in there AFTER the birds have been in the pen for a few weeks/months dropping waste that you now find yourself crawling around in)
As Ol Grey Mare has already said, there is no one way that is best for everyone. I keep both my food and water outside the coop, but I have a place to put the food where it will not get wet in the rain or snow. The girls don't normally go back into the coop during the day unless they are laying.
it's a matter of trial and error. You try something and if it doesn't work as well as you'd like, you try something else. I certainly don't have the same feeder or watering system I started with 3 years ago. I don't even have the same coop. What I use now seems finally to be efficient and easy to use for me. We'll see how it all works this summer.
I do keep feed inside and water outside the coop. I however found that in the winter the water needed tended more outside in the run than I liked. I also found that they did NOT want to go out on very cold or windy winter days.
Now I keep the feed inside year round and water inside in the winter. Yes this can cause additional moisture in the air. To limit that issue I dump the water every evening when they go to roost and am out before sunup to fill with fresh water. I open the pop doors at that time as well as keeping a LOT of ventilation open year round.
I have my chickens' food and water out in the run. The run is as predator proof as we could possibly make it. It's a hoop made with cattle panels and covered in chicken wire and hardware cloth, with a hardware cloth apron extending out two feet. So I leave the pop door between the coop and the run open 24/7, 365 days a year. The run is covered with plastic (think greenhouse) and we have power hard wired in to both the coop and the run, so running a stock tank heater is no problem.
As has been so well stated, what works best is what works for you and for your birds. Period. What I do may seem nuts for someone living in Northern Wyoming, but it's the system that works best for us. It may well not be for you. Last winter we had the waterer in the coop. We changed that this winter. So, as @wamtazlady said, try what you think you'll like, and if it doesn't work change it. It's as simple (and as complicated) as that. I've made so many changes in how I do things that my setup now bears little resemblance to those hastily scribbled plans on a piece of graph paper! Good luck!
We have a big galvanized hanging feeder we put out in the yard each day, and a nipple watering system along the outside of the coop. But I also built a smaller feeder out of scrap wood for inside that's always full so we don't have to put the big one out on rainy days, and I still keep a 2-liter soda bottle with a nipple on it inside as well. We used these when they were chicks to get them used to drinking from the nipples. It doesn't take up much room, and that way, they'll never be without a source of water whether in or out (just in case the door fails to open and they get stuck inside, or some other oddity like that). The feeder fills through a 4-inch pipe in the wall behind it that we fill up from the storage side of the coop.
I keep feed and water inside coop.
My coop is large and waterer is a closed jug with horizontal nipples and heater in winter, run is not solid roofed.
Feed is stored inside shed where coop is, so it's easier and I don't have to worry about weather ruining feed.
Plus I use supplemental lighting in winter, so they are up and eating way before I head outside.