11.91 light-years away
Tau Ceti
Which nearby star is most like the Sun, and why was it the first we listened to?
If you want a star like ours, without a companion complicating things, this is the nearest one. That combination has made it a target since the very beginning of the search for other civilisations.
Sun-like, with caveats
Tau Ceti is a single star of roughly the Sun's type, a little smaller and cooler, about twelve light-years away. Most of the Sun's nearest analogues are in binary or triple systems, which makes stable planetary orbits harder to reason about. This one is alone.
It is also considerably poorer in heavy elements than the Sun, which has consequences: less material for building rocky planets. And it is surrounded by a debris disc with roughly ten times the Solar System's complement of comets and asteroids, which would mean a much heavier bombardment rate for anything orbiting there.
The first thing anyone pointed a radio telescope at
In 1960 Frank Drake aimed the Green Bank telescope at Tau Ceti and Epsilon Eridani, listening for artificial radio signals. Project Ozma found nothing, but it established the method and the field.
Planet claims around Tau Ceti have come and gone repeatedly since; the signals are at the edge of what the measurements can resolve, and the star's own surface activity can imitate a planet. Some candidates are still considered plausible and none is beyond argument, which is a fair summary of how hard this work is at even the nearest stars.