Little Diomede Island (U.S.) in the Bering Strait (not the Aleutians, as I mistakenly wrote earlier) is reckoned to be some tens of thousands of kilometers west of Big Diomede Island (Russia), despite the obvious fact that Little Diomede is about four kilometers east of Big Diomede.
The reason for that is that in the state of nature, Europe is east of North America, which is east of Asia, which is east of Europe. So it makes no sense to ask "Is X east or west of Y?" unless we have instituted a convention of some sort.
One possible convention is: "X is east of Y if and only if the easterly great-circle course between them is shorter than the westerly one." That's the rule we apply in ordinary life, and by that rule, the Russian island is west of the U.S. one.
But the navigator's convention unwraps the globe at the 180 degree meridian, and says that the entire Eastern Hemisphere is east of the entire Western Hemisphere. Using this convention, the Russian island is east of the U.S. one.
And by the same token, Alaska, since it sticks into the Eastern Hemisphere, is the easternmost U.S. state as well as the westernmost and the northernmost. The southernmost state is Hawaii. Of the 48 contiguous states, the westernmost is Washington, the easternmost Maine, the southernmost Florida (thanks to Key West), and the northernmost Minnesota, due to a surveying error.