My Ginger was a mutt from a shelter.
She would do anything you wanted to do so any game was her favorite.
The two we enjoyed most was tug-of-war with old tied-up socks. I would just have to say "You know what I'm going to get" and Ginger would know we were going to have a sock fight. We even had "rules" that each of us knew and even if I broke a rule it didn't stop Ginger from her mission to get the socks. The other game is throwing a tennis ball either outside or down the hall in the house. She would play until I got tired. Ginger was a great dog to have as a companion.