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.
Advantages: All stars are about where you would expect them to be relative to Coreward or Rimward. All stars are at their true distances.
Disadvantes: Since it is 2D, stars that are actually fairly close together in the visible sky may be on opposite sides of the map. This happens if they happen to be close to the galactic plane. Unfortunately Castor and Pollux fell into this category, so rather than being fairly close to each other, they end up on opposite sides of the map. I hand moved that one, but I am sure there are others that I missed.
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.
If you change the Hex size from 1 parsec (3.26 ly) to 5 ly, you get the standard density of stars near Earth.