With my first character, Lydia would hang out in the Jarl of Whiterun's palace until I bought Breezehome, and then she moved in there. With my second character, I don't own Breezehome, but I do own Honeyside. I dismissed Lydia and went to find her later, but she didn't appear in either location.
I assume I simply haven't waited long enough, but I would like to know where to expect her. How does Lydia determine her home?