Brothers
A downtown institution for over 3 decades, Brothers is a fav among locals, as well as the tourists who are savvy enough to stop a local on the street and ask them where to eat. 

Brekkies and lunch only (I think they close around 2).  Weekends can be tough finding a table unless you get there early, and there's not a lot of space to wait while one opens up. 

Very veggie-friendly:  all of their breakfast scrambles can be made w/  tofu; there's always a vegetarian soup of the day; their zucchini & almond burger is yum-city; and they've got like ten different salads. 

They do serve meat and seafood, though.  PC alert:  all their chicken and beef are hormone & antibiotic free, and their fish is wild-caught.

My favourites here:  bagel & lox platter (old school - I love it); huevos rancheros (they have a version with chorizo, too, if you're into it); the albacore salad (good quality fish and a pretty, composed plate); and the wild salmon scramble (I sometimes ask that the pesto be substituted with spinach, as even a fantastic pesto can be a little hard to face too
early in the morning). 

Their breakfast sides offer sliced tomatoes or refried beans as well as the more typical hash browns.

The cappuccino is lovely, and their Brothers Mothers Chicken Soup is famous.