Here is a web app that displays nearby systems.
With route calculation in place, this part is not relevant anymore:
It is still in an early stage, and is quite useless for anything else other than virtual stargazing, but shows that even a 3D map can be displayed in 2D reasonably well. Currently it displays at most 60 stars within a 25 Ly radius. (Seems to work with Mozilla and Chrome) If there are many systems nearby, only the 60 closer ones are shown, to avoid overlap. For example around i Boötis only the stars within a 20.5 Ly radius are shown.
The maps are created using the X and Y coordinates of the stars. Then a simulation is performed, with all visible stars acting like having an electric charge, and pushing each other around until all names are visible.
Special thanks to forum members kfsone, Smacker, Codec and Chromatic for their work and inspiration for my project.