I have scoured the tunnels leading to what I thought was Vault 87, but cannot gain entry any further. On my way back to the 'kids' area I found the room on stilts with a powered door with '87' on it. The screen there says it has no power. The door needs a key. How do I proceed from here?

If you want to use that door, you have to talk to Joseph, he is down in the Great Chamber, I think. He will power up the terminal that is to the left of the door. You need either a 50 or 75 science skill mind you. I don't remember, I think it is 50.

Alternatively, you can talk to soldier kid who let you in the settlement at the gate. Ask to use Murder Pass, follow him and he and Princess, a girl, will open another gate. Follow that path and you will have no problem getting into Vault 87.

Don't forget to talk to Biwwy along the way. If you have the Child at Heart perk, you get a prize for free, if not, you have to pay for it. And, though it's a pain, at least for me (I get lost in that damn place every time), talk to Eclair and Lucy. There are ways of making serious caps here. Aw hell, just talk to everyone in there.