4.37 light-years away
Alpha Centauri A
What would our nearest neighbouring sun look like from a planet going round it?
The closest star to us that is genuinely like the Sun. It is also not alone, which is the interesting part.
Three stars, two of them familiar
Alpha Centauri A is slightly larger and brighter than the Sun and of the same general type. Its companion, B, is a little smaller and cooler. The two orbit each other on an eccentric path over about eighty years, coming as close as Saturn is to the Sun and drawing out to beyond Pluto. Far out from both, Proxima completes the system.
From a planet orbiting A, B would be an intensely bright point — far outshining anything in our night sky, bright enough to read by, but still unmistakably a star rather than a second sun.
The only realistic destination
Every serious proposal for reaching another star names this system, for the simple reason that it is the nearest one. Concepts involving light sails driven by ground-based lasers aim at crossing in decades rather than millennia, though nothing of the kind has been built.
The southern sky gets the better view: at −60 degrees declination the system never rises for most of Europe and North America. The nearest stars to the Sun are, from the majority of the world's population, permanently below the horizon.