distances - Where can I look up the 3D positions of the closest stars?

You can determine the 3D position for a star, $p$, by using the distance from Earth, $R$, as well as the right ascension, $Omega$, and declination, $delta$, within the following formula.

$p = R begin{bmatrix} cos Omega cos delta \ sin Omega cos delta \ sin delta \ end{bmatrix}$

Note this will yield positions within the Earth-centered inertial reference frame.