The birds in this part of California don't really leave. There's a park they all go to and there's lots of visitors that come by and feed them, so they just all stay there all throughout the winter. It's really nice because there's various ducks, swans, peacock's, and other tropical birds, but it's the geese you have to be careful of, they are mean and they won't hesitate to chase you down if they see you have food, or if you get too close to them, or if you're close to one of their hidden nests. They will attack you. Even if you are on the water in a boat they will attack.
For the little common birds and crows they sometimes leave, but we once had some little birds that decided to nest in our trees and they would attack our dogs and steal their food, so eventually we had to put up tarps to block them from getting our dogs and their food when they were outside. I would suggest late winter, early spring when things start to warm up in your area cause they will be hungry when theyve migrated back in your area. It is a long journey for them. Good luck!