I think you are probably placing the cart in front of the horse. Although getting to a new undiscovered place is nice and getting your name placed in a system is rewarding, try to set off to a mini exploration first, as a practice.
Take Orion Nebula, or any other close by -500ly to 1,000ly dist.- and feel the expedition. Get used to your ship, understand distances and what they mean, understand the different bodies, and stars, and scooping, Scan vs. detailed surface scan, payouts, where to sell data, etc. Get all the practical things of actually exploring out of the way first.
The mini drill will allow you to see what does really mean and what does it take to be the first explorer -for once- and also the pay outs but most importantly, your patience and endurance in going out for a 1,000 - 5,000 or more ly trip.
e.g. I have a few hundred thousand ly under my belt as explorer and many thousands of first discovered astronomical bodies; however, my last exploration thru the galaxy took me almost 4 months, but I now enjoy urban exploration, and I don't care about first discovered tag because I still get paid and get a lot of fun.
By then, you will have a pretty good idea where to go, cause in reality, you can go anywhere and you are sure to find virgin systems.
But if you definitively want to know at least one of millions of possible directions...hmm...I would probably head below the Galactic Plane and -with SAG A* at 6 o'clock from SOL - I would head 10-11 direction.