At any of the signature restaurants, or most other table service, just make sure you tell the server when being sat (we've often been asked). Both times that we've been with someone with a nut allergy (at Jiko and AP), the chef came out, talked the diner through the menu, going over what is safe, what are the better options. At the counter service, you will have to be more careful. I'd suggest going to Guest Relations and asking if they can give you list of safe items for each park. FWIW.