Hey everyone. A lot of us have had this issue. After you recruit Curie as a companion, she won't go to your settlements. You can command her to go to one and you'll get a notification saying that Curie is going to Sanctuary Hills (or whatever other settlement), and you can even watch the population count go up by one. However, she just goes back to Vault 81 and stands in front of the doctors office. I'm in a second play through now. It took about an hour and a whole bunch of reloading, but I found a workaround. It doesn't involve console commands or anything like that, so I'm assuming it should work regardless of the platform you're on.
There will be some potential spoilers for the Hole in the Wall quest here, but I'll mostly be avoiding them since the actual nature of the quest is mostly irrelevant.
You pick up Curie in the Hole in the Wall quest. Work through the secret portion of Vault 81, talk to Curie to get the Vault 81 Cure, and then head back up to the main part of Vault 81. Curie won't yet have any interactive dialog since she is not yet officially available as a companion. Your next task in this quest is to bring the cure to Doctor Forsythe. Talk to Doctor Forsythe and hand over the cure. Once you do this, you'll get a notification for the next task in the quest to 'Talk to Austin'. DO NOT talk to Austin yet. As soon as you hand over the cure to Doctor Forsythe you also get a notification that Curie is now available as a companion. As soon as you get this notification, talk to Curie. She'll go through some dialog, and you'll have the option to ask her to join you. Ask her to join you, then immediately talk to her again and dismiss her to whatever settlement you prefer. She should then float her way up the stairs and back to your settlement. After this, you can go talk to Austin and complete the quest. Once completed, fast travel back to the settlement that you sent her to and sleep for 24 hours. When you wake up, you should find her floating around somewhere.
By talking to Curie immediately after handing over the cure, you're going to miss out on a bit of dialog between Forsythe, Austin, and the Overseer, but given a choice between hearing this dialog or actually having Curie at a settlement for the rest of the game...the choice shouldn't be hard to make.
Factors that could possibly be relevant - You have the option of splitting the cure or keeping it for yourself rather than giving it to Austin. I have no idea what will happen if you do this (because I'm not a heartless monster ), so I suppose it's possible that this could change the outcome. I doubt it, but it's a point to consider.
Holt Combe and Tina De Luca are both technically recruitable, but bugged. The dialog with Alexis Combe that is relevant to the Holt and Tina thing is also bugged, and I avoided talking to any of these characters until after successfully sending Curie to a settlement. I still couldn't recruit Holt, but I did manage to recruit Tina by choosing violent dialog options with Bobby during the Dependency quest and provoking him to attack me. This seems to be the only way to recruit her and have her actually show up. Tina is at Sanctuary Hills and tending some crops now, but she doesn't talk. This seems to universally be the case for everyone that's successfully recruited her. I'm not sure if avoiding talking to them until after recruiting Curie played a part in any of this, but there's no real reason that you need to talk to them prior to completing Hole in the Wall. I'd play it safe and avoid them until after you finish it.
In my first play through I was never able to get the Short Stories quest with the schoolteacher in Vault 81. I'm not sure if it's related to any of this, but I was able to receive that quest immediately after completing Hole in the Wall this time. It may or may not be related to the Curie bugs.
Not having Curie at my settlements during my entire first play through was a really annoying bug for me, and I'm really glad to have her there now. I know this has frustrated a lot of other people who find Curie to be as adorable and lovable as I do, so hopefully some people can find this useful in future play throughs if it doesn't get patched first. Now I'm off to do some traveling with Curie.