There is a new farmers market near my parents house that has a petting zoo! It's called Good Neighbors Farmers Market. It's $2 to get in per person, but that includes excellent parking, petting all the animals they have, and some really nice vendors. They have a beautiful barn and all of the vendors inside either grow or make their products within 50 miles. They also have live music, real bathrooms, picnic tables, and food trucks.
It's really a fun place to go, and I'm assuming kids would love petting the animals. You can also rent this place for events. Why, why, why are there so many places, restaurants, and resources I would have LOVED to use for my wedding that didn't exist in 2009?!