Woah, a full readable printout of the galaxy in frontier would be something
but quite pointless as there are only relatively few systems that are inhabited, once you get so far away from the Core Systems all the planets are uninhabited so theres literally no point to them all really
I found this out when my ship did a jump drive malfunction and my ship ended up so far away it would have taken about 2 years of game time to jump back assuming I had the fuel and yearly servicing.
Anyway, the imperial systems are directly below (or south if there is such a direction in space) the Core systems.
The easiest way to find the Imperial systems is to centre the star map on Sol, then hold the down arrow so the map scrolls down until you see the purple "Imperial Systems" sphere of influence and near the center of it you will find the "Facece" system, to the right of this you will find "Achenar" which is the Imperial Capital.
I like the Imperial Trader vessel, its good for missions where you need big weapons and speed
A great game it is an all.