The premise of the system is this: the whole thing is covered in super deadly dark matter. Going off into the dark straight to the destination will kill you. To get through it, you have to read the environmental clues, like what directions buoys are pointing in, to navigate through the few narrow safe passages that lead throughout the system. The areas around the JHs should be safe-ish, but be careful where you zoom off to.
You can reach Ames Research Station this way, as well as the other jump holes and points of interest.
Alternatively, if you aren't in the mood to go through the death maze, Galileo remains as your easy bypass to Kepler. If you want to stick with it and are having trouble, try asking around for a guide to see if anyone bites.