Not every state has a great state fair, so I'll take you to Indiana's.
This is a wonderful opportunity for child and adult alike to experience farm animals.
As far as fair food, if it can be fried, it will be. If it can be put on a stick, it will be, too.
We always stop at the dairy barn that sells ice cream, milk shakes, and grilled cheese sandwiches. It is run by 4-H members. I was in 4-H as a kid, as were my children, and we worked at the local 4-H food stand each year. I recommend it as probably the cheapest place to eat and profits go back to the 4-H organization.