Air ambulance providers often work closely with the administrators and social workers of hospitals. Patients who need advanced or specialized care are routinely taken to hospitals where they can receive the care they need. For instance, a cancer patient may go to the Mayo Clinic in Minnesota for treatment.

I have found this link below to pages with a list of hospitals and rankings to be helpful when considering hospitals around the United States:

Hospital Rankings - U.S. News and World Report's Rankings of Hospitals

Hospitals Transfer Patients Themselves

If a patient has no money and needs to be transfered via air ambulance, it sometimes makes sense for the hospital to pay for the transfer. The cost of an air ambulance can be quite expensive, so the benefit of transporting a patient must be greater than the cost for hospitals.