Going out a few hundred lights there are a few candidates for the most unusual systems. An obvious candidate would be Sol - harboring a planet that supports complex life and even intelligent life has to count for something.
My next candiate is Ef Eridani - a 17th magnitude (read -- really dim) white dwarf about 300 light years away that brightens to 14.5 every now and again.
A recent study by Tom Harrison et. al. used Keck II and Gemini North to look at the infrared spectra of the object. What they found was astonishing. Most of the IR is from cyclotron radiation driven by a magnetic field that is more than ten million times stronger than the Sun's magnetic field. They also measured the heat signature of a small companion object that has about fifty times Jupiter's mass. Its composition suggests a nearly exhausted stellar core. It is about twice the distance from its primary star as the Moon is from the Earth and has a "year" that is 80 minutes long - that's about 18 new "years" per Earth day.
The smaller object may be the final resting state that cataclysmic binaries evolve towards. The secondary star shrinks to a substellar mass and lacks the energy to drive mass transfer to the primary.
Not the most comfortable place in the Universe.