Acey,
I am not sure how much we can help with a local installation... almost every time I have heard about login/logout issues, it has been due to session issues and some misconfiguration of the server... but without actually seeing the issue and being able to test, I am not sure what we can do....
You can TRY deleting your cookie on your local browser, changing the cookie name (in the admin tool or directly in Settings.php and truncating the smf_log_sessions table in the database
then try logging in and then out again...