Kind of "semi-systematic", when I want to explore the immediate vincinity, I simply select the closest (relevant*) system in the Nav panel, and check whether I was there already by looking at the destination info that is seen in the bottom right of these screenshots. (it's the bottom right on those screenshots while looking at the Nav panel, but it would be the bottom left of your main screen)


Unknown - I was not yet there
None - I was there already
Obvoiusly that only covers systems that I have visited.
*Relevant: Usually I do this, when I find a high value system or an ELW. And as Redfox mentioned, what I do then is I pick the closest system in the same boxel, as in assume in the "Unknown" screenshot I found an ELW in the current system HYPOAE CHRAEI FA-Q D5-108. In that case, based on the screenshot I would then pick HYPOAE CHRAEI FA-Q D5-430. If that was known (="None"), I would pick 864, and so on. Usually the resulting pattern is a winding snake of visited systems in one general direction.
If I am particularly picky and want to only visit such systems with the same star type, I also pay attention to the Info panel in the top right after "charging" the jump drive - wrong star type? Abort jump and pick next system...