Best is a tough one. My favorite is probably Bills in Surry Hills (http://www.bills.com.au/) - simple food done to a really high standard. Corn fritters or just their scrambled eggs are a must.
Also, people seem to answer this question a fair bit by suggesting Deus ex Machina in Camperdown - Both times I have been there thought the food has been simply average and no better. about 10 years ago
Try Plunge Cafe in Summer Hill (Inner West) - www.plungecafe.com.au
They do a really good all day breakfast on the weekends (try the frittata, it's amazing!) and the best coffee in the area. Service is quick and the staff are really friendly.
Gets quite busy on the weekends, but I've always managed to get a table. - You have the option of sitting out in the sun at the front people watching, sitting indoors or out the back in the courtyard which is a bit more chilled.
And the bonus is that afterwards you can take a look at the cute little shops dotted around the village. almost 10 years ago