Nick Valentine disappeared... what to do?

There is a reddit post with a list of solutions you can try :

• Make sure to look where you originally found the companion.

• Search around the area you last left the companion. They tend to wander around, maybe it just takes some looking.

• Make sure to triple check around the area you sent them, it could be you are overlooking their area.

• PC users can use a specific code to teleport to them. Try player.moveto (NPC ID) remove the parenthesis.

• If you have most dog meat make sure you check your doghouses, he usually hang around the ones that are a bit distance from the center of the sanctuary.

• Generally if you realized you lost a companion, try to retrace your steps, and go back to the last quest, or area you were at. They could be just standing there like bums.

Othersise, you can build a bell and try this :

[...] If you go into the workshop menu when you’re at a settlement, head over to Resources> Miscellaneous, go two across, and you’ll come across the bell. Build one of these on your settlements and it will gather all of your nearby settlers when rung. Make sure it’s built in a central area where people can gather around it. This is the best way to try and get back any of your settlers who have gone missing, or just as a means of organizing your workforce for the settlement chores, as everyone eventually (although slowly) makes their way towards it. (source)

And finally, you can read this, but be aware that you may be spoiled :

"I have the same problem. I sent him back to his office but he isn't here now even after waiting over 24 hours. Edit: I figured out where he was! I dunno if you're at the same part of the quest as me, but on Reunions where you have to tell Piper about your findings, when I showed up in her office he was there too."