So I've just spent a bit of time working on my pathway around New Eden. The map to the left (click on it to enlarge) shows the route I'll be taking, which takes in every single region of New Eden without going through the same region twice.
I'll be doing this mostly in my pod (sometimes I'll be in a shuttle...). Over 5,000 systems.
I'm starting in Curse, and ending in Curse. I don't know how long it'll take me, but I will complete it. I'll be taking photos in every system and compiling them into a database of sorts. Not sure how yet, but I'm confident the details will work themselves out over time.