This keycard is used to access the cave in Vault 22. The cave is the only way to get to the 6 HEPA 20 cartridge filters you need to complete the quest Still in the Dark. You can also find mantis ootheca containing the giant mantis eggs needed to complete Bleed Me Dry. The keycard is required to get into the server room, which access is needed to to get research in the quest There Stands the Grass.
In Vault 22, on the fourth floor/common areas (lower level), turn left as you enter the lower level and a bit further on, there is a door with a sign that reads Quarters. This door is locked with an Average difficulty lock, but can also be bypassed using the terminal in the overseers office. Past the Quarters door, the keycard is located in the first room on the left. Just inside the room door on the right is a shelf. The keycard is sitting on a stack of papers on the shelf with the lamp.
While it may be convenient to use explosives in the rooms to try and badger out the spore carriers, this can cause the keycard to be flown to another location in the room, forcing the player to rummage around in thick flora in order to obtain it.