If bought, Gracie can be sent to any workshop settlement that is under the population cap, and will count for five points of defense. She will also go into a doghouse to rest just like Dogmeat.
When looking to find Gracie at the settlement selected when purchased, she will be found at any available doghouse. One can remove all existing ones then place a new one where the player character prefers her to be located.
In the workshop interface the Sole Survivor can select/move the doghouse and she will follow around while carrying it.
Possibly at higher levels, Gracie can spawn as a glowing mutant hound and gives off 1-2 rads/sec when the Sole Survivor is standing right next to her.