At the log in screen, you can select a Start Location of "My Home", "Last Location", or a region name typed in manually.
A convenient addition to this list would be the locations stored in your character's "Picks" list. That information could be cached at logout, the same way that the screenshot of your home and last location are cached.
Since a Picks list is public information, there is no concern that a second user on the same computer would get access to any private information before entering a password.