I believe there are 3, the Bridge for Raiders, the Vault path area for Supermutants, and Water for mirelurks. I've only got around 15 hours in the game so there may be more. It's worth noting that on my first character I was never attacked there, it only happened after I bumped the difficulty up.
Okay, so first off, it ought to be known that the vast majority of companions do not have quests in the traditional sense. Most are recruited through a quest, but those quests don't have any special conditions for the most part. You can get each of their companion perks purely by raising their affinity for you to the maximum.
Those that do have a quest, are Nick Valentine, MacCready, Curie, and Cait.
MacCready, Curie, and Cait's requirements are strictly affinity based. All you need to do is raise your relationship status with these three, and converse with them regularly. They'll let you know when they're ready for the next step and tell you what you need to do.
Nick Valentine is the outlier. In order to do his quest - Long Time Coming, You'll need to have advanced the main quest past the quest Dangerous Minds. Specifically, after you've tracked down Kellogg, you'll need to visit The Memory Den in Goodneighbor with Nick. Additionally, you may need to first complete one or both of the other detective case files - The Gilded Grasshopper, and The Disappearing Act. You can pick up both of these quests by examining the files left lying around in Nick's office in Diamond City. He doesn't need to accompany you while you do them, but they offer some good opportunities to make Nick like you more along the way.
After you've completed those three quests, and maxed out your affinity with Nick, he'll offer his quest.
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Pretty sure the post indicating you can have the implants installed by the Institute is a hoax.
I have completed the institute endgame (and non-radiant side quests) and talked to every named NPC in every division (nobody was killed or exiled), none of them mentions the implants when they are in my inventory and no doctors have this as an option in any sub menus.