Be wary of terms like "organic", "cage free", or "free range" on supermarket eggs. Organic simply means that the chicken is eating organic feed, they can still be living in cramped, indoor barns. Cage free is equally ambiguous. A barn crammed full of chickens, without basic sunlight or fresh air, can produce "cage free" eggs.
Your best bet is to find a local farmer that can supply you with eggs. Go visit them. Any time we've ever moved I've had to source our farmers to supply us with the quality of food we wanted. It's a wonderful experience to speak with the people that produce your food, to share in their passion. We've been so grateful to have made such incredible friendships through our search for healthy food. It's also a wonderful experience to share with kids. Teaching our children what healthy animals look like, how they are raised, and how we can make a difference by purchasing food locally is a benefit to them and their communities in the future.