what is the typical finished height of a breakfast bar?
You might want to check out www.am-wood.com and look in their archives they have plans for a breakfast bar there.
It should depend on your personal parameters. How tall are the people who will be using it? How tall are the chairs or stools you will use at the bar? Do you want to use standard off the shelf cabinet bases or custom units? Do you want a bi-level breakfast bar which hides the clutter on the other side? How will the bar height relate to other parts of your kitchen? Do you want to store anything in particular underneath the breakfast bar? etc....