Except in midsummer, I always take a jacket with me whenever I leave the house. I live in a cold, wet place, so if you’re in a more habitable area, you can skip this one. Likewise for people who never lose their keys.
Right now my keys are on a cord, which is about the right length to suspend them
in my pocket. It used to be an adjustable cord, but that didn’t work out; now, opening the door is a very personal experience. Also, when I change my pants, I often forget to transfer my keys.
A roomy, uninsulated, waterproof jacket is a good candidate for three season duty, and should therefore be the safest place for keys. In a pocket though, even a zippered pocket, they are too easy to lose. There is no place on any jackets I have seen to attach a tether which is long enough to reach a lock comfortably, and will not tangle in the pocket.
One way to do this is to anchor a strip of Velcro to the elbow. The loops would run along the sleeve from elbow to armpit, where there would be a little key pocket.
Another way would be to run a longer tether along the side of the coat. Anchored at the bottom, it could share the previously mentioned pocket, which is pretty much it for a waist length coat. A longer coat could be set up to allow the tether to anchor at the armpit. Carried this way, the tether could be plain nylon web sitting in a zippered channel, with no pocket needed.