I was quite pleasantly surprised to find a couple of undiscovered systems near to the Coal Sack on my first jaunt out into deep space. My main mission was to visit HIP 63835 (one hell of a crazy cool system, go there now if you haven't already!), but I decided to push out to a bit past the Coal Sack and then circle back around and return to my 'adopted-home' system (70 Virginis) via the Federation-Empire border. There were discovered systems with undiscovered bodies, but I claimed discovery for one or two entire systems along the way. Managed to discover about 40 or 50 objects from a short 1000LY round trip.
So yes, there is definitely uncharted territory within reach of the beginner explorer. I didn't happen upon any Earth-likes, but there may be a couple lurking around still.