Tau Ceti

Tau Ceti (τ Cet, τ Ceti) is a star in the constellation Cetus. It can be seen with the unaided eye as a third-magnitude star.
It has a spectrum similar to the Sun, but is only 78% of the Sun's mass. It is just under 12 light-years from the Solar System, a relatively nearby star. It is the closest solitary G-class star. The star appears stable, and is "metal-deficient" because (like the Sun) it is mostly made of hydrogen and helium.
There is more than ten times as much dust surrounding Tau Ceti as in the Solar System. There are probably five planets orbiting Tau Ceti, two in the habitable zone. Because of its debris disk, any planet orbiting Tau Ceti would get far more impact events than Earth. Despite this, its Sun-like characteristics have led to widespread interest in the star. Tau Ceti is consistently listed as a target for the Search for Extra-Terrestrial Intelligence (SETI), and it appears in some science fiction literature.
Searching.
Project Ozma searched for intelligent life (SETI) by examining selected stars for artificial radio signals. It was run by the astronomer Frank Drake, who selected Tau Ceti and Epsilon Eridani as the first targets. Both are near the Solar System and are similar to the Sun. No artificial signals were found after 200 hours of observations. Subsequent radio searches of this star system have also turned up negative.
Planets?
On December 19, 2012, evidence was presented for a system of five planets orbiting Tau Ceti. The planets' estimated minimum masses are between two and six times the Earth's mass. Their orbital periods range from 14 to 640 days. One of them, Tau Ceti e, appears to orbit about half as far from Tau Ceti as Earth does from the Sun. With Tau Ceti's luminosity of 52% that of the Sun and a distance from the star of 0.552 AU, the planet would receive 1.71 times as much stellar radiation as Earth does. This is slightly less than Venus, which gets 1.91 times Earth's. Some research places it within the star's habitable zone. 
The habitable zone for a star is where liquid water could be present on an Earth-like planet. For Tau Ceti, this is at a radius of 0.55–1.16 AU, where 1 AU is the average distance from the Earth to the Sun.
References in Science Fiction.
The Expanse (TV): Destination of the Nauvoo, on a 100 year voyage. The ship is 500m cylinder, 2000m long. It would require a continuous acceleration of 0.05 m/s for 50 years, and an equal deceleration at the halfway point.
The Foundation book series by Isaac Asimov: The home star of the planet Aurora, first planet to be colonized by humans.