The sectors won't show gates or gate connections you haven't found. You need to actually find the gate for it to show the connection out.
The sector east of president's end, I forget the name but it should have a trading post and a big roid field near the east. Somewhere out in the east is a gate (you should be able to find it by watching where the traffic goes) and that gate will lead you to a lot of Fun places
I would suggest bringing either a fast ship, or a well armed one.
As a rule, watching the traffic lines will show you where most gates are, though there are several which you will have to search for. QUite a lot of unknown sectors out there, unclaimed by anyone, sometimes for good reasons, have a look for them. Some of them make some very nice places to set up your own little bases.
Oh and a triplex scanner will help a lot. Buy one if you don't have one. I think that terracorp HQ sells them in home of light.
