After the sun the closest star to Earth is how many miles away?

Alpha Centauri, which is at a distance of 4.3 light years, or 25 trillion miles.

Sorry. The correct answer is Proxima Centauri, in the Alpha Centauri system.

The closest star system to the Sun is the Alpha Centauri system. Of the three stars in the system, the dimmest -- called Proxima Centauri -- is actually the nearest star. The bright stars Alpha Centauri A and B form a close binary as they are separated by only 23 times the Earth- Sun distance - slightly greater than the distance between Uranus and the Sun.

Source: NASA.gov