Call me a bad American, but I prefer to measure my runs in kilometers than miles. So while I'm perfectly happy to have my driving directions in miles, my weight tracked in pounds, and my temperature in Fahrenheit, all I want is my runs in that other format. Thankfully Apple makes this possible in 2 different ways.
Method 1: On the Apple Watch
This method is quite simple, but took me longer than I'd like to admit to discover (big shout out to @tedsvo for the tip!). Simply go into the Workout app on your Apple Watch, tap on select the type of workout you want to start, and swipe over to the distance goal. Force press into the screen, and you'll be prompted to select miles or kilometers.
Method 2: On the iPhone
This is a little more involved, but accomplishes the same thing. This method requires you to make a change to the Health app on your iPhone.
Once you open Health, tap on the big Activity header image, then go into "Waling + Running Distance," tap "Unit," and choose what unit you would like to use.
Once that's done, there is nothing left to do. Your watch will pick up the change and automatically change all foot-based workout measurements to miles or kilometers.
As a final note, watchOS 3 and iOS 10 require all workouts of a certain type to be the same measurement. In other words, you can have your runs and walks in miles or kilometers, but you can't have runs in kilometers and walks in miles, you have to choose one or the other. And yes, that does include treadmill workouts.
The good news is that biking and swimming workouts are broken off from each other. If I wanted, I could have my runs/walks tracked in kilometers, bike rides in miles, and swims in kilometers.