When searching for hidden jump holes to other systems, turn on your Nav Map, then select the "Show Patrols" map. The lines that appear show popular paths that the AI ships use. Almost any path that stretches out beyond the normal trade-lane traffic of a star system will lead to a hidden starport or even a hidden jump hole. Fly out to where the line leads to and turn on the "Solars" option on your targeting computer. You will usually find a place of interest but in places with reduced sensor ranges you will probably have to rely on visually looking for something. Also, to find all the paths, make sure to look at the "neutral", "hostile" and "friendly" paths in the patrol paths map. Be wary of stumbling upon an enemy's base.