May I go classic and boring?
But if you want to just thread the waters of exploration on one or two afternoons...go to the Pleiades.
Sure, by now must be all claimed but:
-It is very easy to get there
-It has diversity...there even is a Black Hole (Won't tell you, find it!)
-It is relatively quick, you can do it in a couple or three game sessions there.
-You can easily point to the sky in real life and brag with anyone how you flying there and what you have found.
-It gives you a little taste of what a longer exploration might be.
Only con is that you probably will hit traffic or even NPC interdictions every now and then as is not that far from the civvy space.
After that, you can try Orion Nebula, and keep growing distances from there.