Sorry, but that's not possible when you have more than one user account on your computer.
When you say local account, is that a "standard"
account type?
If it is a standard account, then you could delete your standard user account to only have the one administrator account to use like this instead if you like since you can't delete or disable/hide your only administrator account and no not want automatic log on. Be sure to backup anything in the standard account user folders that you do not want to lose first though.