Lunch before Hamilton Art Gallery
I have always liked La Luna (as per Mike from Hamilton). Believe it or not, Hamilton also has a fine sushi restaurant: Hoya Korean & Japapese Cuisine at 161 King Street. They do these fanastic steamed shrimp dumplings (I think they call them shumai, but they should not be confused with the dim sum of the same name) that I can rarely find elsewhere.
It depends on what you are looking for:
The cafe on the second floor is exactly what one would expect from a cafe in an art gallery - light fare at slightly higher than normal pricing...
Papagayo - Mexican on King at Hess St. Not overly spicy or firey foods, but flavourful.
La Luna - Persian/Mediterranean on King at Queen St.
Dalinas - Persian/Egyptian on King William
Wild Orchid - Portuguese on James St. N.
Room 41 - King William, fine dining
Capri - "Old School" Italian on John St. N. they have a great antipasto platter
Just don't expect anything in Jackson Square unless you want to eat at the food court, have the lunch buffet at the hotel or try your luck at Walt's or Toby's Goodeats...