I think Bar Tartine for brunch is a good choice. They open at 11, and you can make a reservation. Considering that this meal won't happen until after 11, you might not really need that much lunch. For what it's worth, my Australian food-loving friend who visits the USA loves Bar Tartine. Get the fried flatbread (I generally like the savory versions more than the sweet) and the smoked potatoes.
If you need a snack prior to that, you could check out the farmer's market at Civic Center, which is on Sundays. Not like the Ferry Building, but still interesting to walk through and there will be some good fruit samples at that time of year.
I would skip Mission Chinese....instead, check out some of the Sichuan or Xi'an options while you are in New York City.
I think breakfast at the Mill before Alcatraz is a good idea. It's not particularly on the way, though, but from where you're staying you could take a quick bus-ride there, or an even quicker cheap taxi ride.
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