Faneuil Hall does have a _large_ food court.....but if you are after either quality or authenticity, walk through Downtown Crossing up to Chinatown, or get on the State Street Orange Line and get off at Chinatown, and feast your little heart out for less money and more quality.
Any of the cheap places will serve you just great, like Pho Pasteur, but if you are wiling to pay a little more for something a little different, try Penang or Ginza.
Or you can walk north on Hanover Street, and be in the North End. Tons of high quality Italian food, of all price ranges.
If you have the time, and you've dragged your carcass all the way down there, the extra walk or ride is worth it. IMHO : )......