I DID make a 2D map of near space that I like, but I had to make several assumptions that others may not agree with that could make it work or not work for someone else.
I used the HYG star list, converted everything to galactic XYZ coordinates and distance. I then used the X and Y values to calculate an angle called THETA (for lack of a better term). Where 0 degrees Theta was Coreward. I then plotted all the stars using Theta and the true distance.
Hmmm... Could you just use the X and Y coordinates and ignore the Z? Distance would be inaccurate, but relative locations on the X and Y axis would be accurate.
MAJOR DISADVANTAGE: Actual number of stars goes up with the cube of the distance from Earth, but in a 2D map, it only goes up with the square of the distance. That means that the farther from Earth you go, the denser the stars get and you end up with many stars in every hex. To fix that, you can drop a lot of those dim M stars, or stars without names (just numbers). Things really fall apart after about 40-50 light-years and beyond that you might as well make things random and just keep a few of the brighter stars for reference.
Another option I'm thinking about would be to ignore most flare stars - which are unlikely to have life or even be colonizable due to massive solar flares occurring from time to time. Am I correct?