The nearest known planetary system (that isn't the Solar system) is that of Epsilon Eridani, 10.5 ly away.
The nearest known planetary system (other than the Solar system obviously) with a theorized habitable planet (in hopes of it stabilizing large bodies of liquid water based on temperature estimates) is Gliese 581, 20 ly away.
Proxima Centauri is not known to have any planets...it hasn't yet been on the radars of planet hunters.
Alpha Centauri A & B are the nearby binary star system, which are both more likely to have planets than PC, and are recently making their ways to planet hunters' radar.
ACA & ACB are the binary star system. PC bears a distant connection to them, but the extent of PC's connection is unknown. Maybe PC is the tertiary star...or maybe PC is on an escape trajectory, and only during the century of our knowledge of it, it happens to be nearby the Alpha Centauri system.