XXYY is right about the bacteria concept. The oil and grease might be bothersome though. I would avoid working at fast food places because of that unless I had absolutely no alternatives (that's legal haha!). Though, I did work at my uni's dining hall and did okay but it wasn't a really greasy environment and I didn't cook food.
Yeah maybe Subway would work? Starbucks? You could try "healthy" fast food places (like Garbanzo's or Chipotle) or places that make a lot of sandwiches/ subs where you don't really fry stuff. Or ice cream/smoothie places, like Dairy Queen or Jamba Juice. Bakery places, like Panera might also be okay.
Good luck on your job hunt.