If it is the key to the caves you're missing, it is on the first room on the left in the corridor of the lower living area. The one with with a baby carriage in it.
When I enter Vault 22 the door to go from Main Entrance to 2nd level (where Nuka Cola Vending Machine is located) is not locked, but coming out it is locked. I had picked up the key earlier but now apparently don't have it. Can't escape Vault 22. Frustrating. I verified cache and every time I do it finds one missing file and reacquires it. I wonder if my Glary Utilities is removing a file.