You can't get more local than the Blue Moon Diner. It's on Main Street in Charlottesville. Traditional diner food and some inspired twists. Not to mention the infamous Elvis lamp and great music still played on vinyl.
Bluegrass Grill, also in Cville, has very good food and has a more natural approach to breakfast. Not as much grease and bacon, though they do offer some of that too.
Another very local place is a real favorite of mine: Beer Run. They make good food like breakfast paninis and burritos and have a full bar, not to mention a huge amount of great beers on tap. Everything is made on site and is delicious.
Higher end brunch type places would be Maya, Horse and Hound, Boar's Head, etc.
Blue Moon Diner
512 W Main St, Charlottesville, VA 22903