It's misleading when the main star is ID-ed as the mission location; the actual location can be anywhere. I'm not sure why this is true.
I always use the FSS to find mission sites. I find it to be far quicker than stopping at the nav beacon the majority of the time.
It's quite simple:
Honk the system
start your FSS
tune to the far left part of the range (where non-planetary goodies show up)
scan around the system normally (I usually follow orbit lines first) *
look for an orange circle (rather than the normal white) Mission sites aren't always along orbit lines, but they seem to be (or close to them) the majority of the time (my experience)
once you select the orange circle (feature) the FSS, it will show up in your nav panel list of goodies in the system.
In my experience, once you've done this a few times it becomes very quick to find the mission sites, be they salvage, assassination, or other. This I find to be true the majority of the time.
* Mission sites can be hidden within multi-zoom-step features shown in the FSS so I always syep into those to have a look. Sometimes they'll illuminate in orange before you zoom in, making them obvious, sometimes they do not.
NB: normal color scheme presumed