Feenies, the casual, hip restaurant opened by Chef Rob Feenie, has been known to serve delicious brunches.  
Make sure you book a reservation quite a few days in advance because the place is always fully booked! 

Cafe Crepe has 2 downtown locations, one at 874 Granville Street and another at 1032 Robson. They aren't fancy, but reasonably priced for breakfast or other light meal. For a light Italian style breakfast, try Scuie at 800 E Pender St. The Caffe Artigiano at 740 W Hastings St serves a hot breakfast as well as pastries.

If you really want a budget breakfast, go to Vancouver Community College at 250 W Pender St. The second floor has a cafeteria and reasonably priced food. In summer, it's likely to be closed on the weekend.