At IOA go to Burger Digs in the JPRA section of the park.
It works out perfect because they open at 11am and you'll be hungry when you see it. Get to IOA when they open, take your lap going clockwise (Hulk, Spiderman, Dr. Doom, Rip Saw Falls, PF, JPRA), then see if they are open. If not walk past and do Flying Unicorn or Deuling Dragons and come back.
They sell burgers and frings (fries+onion rings) with a full condiment bar on the side.
It's indoors, and downstairs is a play area for the kids with dinosaurs to look at.
There's a pizza joint nearby, but they're outdoors with fans.