If my son fell 4 stories at JFK and suffered serious injury, does he have a case against the airport?

Your son may have a claim against the airport for negligence.  Negligence is based on failure to  exercise due care (in this case that degree of care that a reasonable airport would have exercised under the same or similar circumstances to prevent foreseeable injury). 

When your son completes his medical treatment and is released by the doctor or reaches a point where he is permanent and stationary which means no further improvement is anticipated, obtain the medical bills and medical reports.  The medical reports will document the nature and extent of your son's injuries and will be used to determine compensation for pain and suffering.  Compensation for pain and suffering is an amount in addition to the medical bills.  Your son's claim against the airport and filed with the airport's insurance carrier should include the medical bills, medical reports and documentation of any wage loss.  Compensation for the medical bills and wage loss is straight reimbursement.  As mentioned, compensation for pain and suffering is an amount in addition to the medical bills.  If your son is a minor, you will need to be appointed guardian ad litem to pursue the claim on your son's behalf.  If your son is not a minor, he can of course pursue the claim himself.  If your son is not a minor and is dissatisfied with settlement offers from the insurance carrier, he can file a lawsuit for negligence against the airport.  He will need to file his lawsuit prior to the expiration of the applicable statute of limitations or he will lose his rights forever in the matter.  If your son is a minor, you will have to file the lawsuit on his behalf as guardian ad litem because a minor cannot file a lawsuit.

In order to prove negligence, you or your son would have to establish breach of the duty of care by not having a barrier or warning to prevent one from falling over the railing, actual cause, proximate cause, and damages.  Actual cause means but for the airport's failure to have  a barrier or warning to prevent access to the railing, would your son have been injured?  If the answer is no, actual cause has been established.  Proximate cause means were there any unforeseeable intervening events that would relieve the airport of liability?  If the answer is no, proximate cause has been established.  Damages means monetary compensation for the injuries such as medical bills, pain and suffering, wage loss, etc.

If your son climbed over the railing, the airport could assert the defense of assumption of the risk  which means your son recognized and understood the danger and voluntarily chose to encounter it.  If the airport is successful in asserting the defense of assumption of the risk, it could bar your son's claim for negligence.  If your son is a small child, the airport would have a difficult argument in claiming assumption of the risk.