Where can I look up the 3D positions of the closest stars? The problem:

I want to simulate a travel from Earth to the closest 15-25 stars. Which is the fastest way to accomplish this?

What i have:

I currently have the distance between Earth and the nearby stars, according to this link: http://www.space.com/18964-the-nearest-stars-to-earth-infographic.html. But from it I can't know if Alpha Centauri (4.3 light-years from Earth) is closest to Sirius (8.58 light-years from Earth) or to Wolf 359 (7.8 light-years from Earth). 

What I need:

I need the distance between any two stars, at least the closest ones to Earth. Then it would be possible to run a Traveling Salesman problem, in order to visit all the nearby stars (or a subset of 15-25 of them) in the fastest time. 

Where can I get this information?
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.