To be fair it is hard, since almost all the new systems I've found thus far, don't have patrol routes. Best bet, is to just fly and look. Set up a grid search.. it may take awhile but eventually you should find it.
Iâll carry this flag
To the grave if I must
Because itâs flag that I love
And a flag that I trust
its always good to have spent some time on at least one char, mapping all the jump holes, sytems (even guard ones) and bases.
heres a screen of my recon char after 3 days of creation:
as you can see ive mapped alot, but i still have some places to go (got rhienland and a bit of the omegas left, and tau)
POTENTIAL SPOILER
also, ive heard that you can use certain softwares (wont name em. tis discovery for a reason:P) to help you map systems (i used one the first time i came to disco, now i know all the systems off by heart. well, most:P)