For me, my home is my house. My city is my home, but that's easy for me because I grew up here AND I currently live here. I don't think of my hometown as my home though... I live more than an hour away now. And my parents have moved twice since they moved out of my childhood house, so their (new) home is definitely not my home.
It drives me crazy when Wagon Sr. refers to his mom's house or his hometown as "home"! Or even if we're traveling, he'll refer to wherever we're sleeping as "home". I guess for him, "home" could be wherever we are laying our heads.
Where is "home" for you?