I read somewhere there is a place called Liberty House Restaurant you can sit outside and enjoy their view of Manhattan and the Statue of Liberty.
Also The
Ellis Island Cafe, a very limited menu here - American and ethnic food, coffee bar and smoothies.
The cafe is indoor seating and an outdoor deck that overlooks the Statue of Liberty, American Immigrant Wall of Honor, and lower Manhattan, location-Ellis Island main building.
Very pricey food I read most of the selections are fast food (their value meals were $9). Not really good comments on this two places i`m afraid.
I would suggest eating a big breakfast and bringing a pack of crackers or granola bar to tide you over until after the tour.
I hope this helps!
Links of interest:
Flights To New York,
Manhattan New York,
Staten Island New York