Closest US states that don't border each other

Some US states come very close to touching, but may fall short by a rat's whisker. Which pairs of states that live so close yet so far apart can you name? If you think that some of these distances don't sound that close, to give you an idea of scale, Maine is approximately 7,999 km away from Hawaii, a distance you could fit the length of Chile from north to south almost twice. To answer, just type the two states that you think may be almost neighbours in any order, e.g. type Florida-Alaska or Alaska-Florida if you think that's an answer (Hint: it isn't!)