My father is 75 and will be having back surgery. He will be unable to drive after his surgery. He is a veteran but has not signed up for benefits. He lives in Staunton, VA with my mother who is in a wheelchair. I live in PA, 5 hours away. Myself and my brother will be there after his surgery when he gets home, but after we leave, we want to try to set up or find out what is available to him for doctor appointments, which will be at Univ. of VA hospital.
There are also services arranged through the hospital (you would want to talk to social worker at this hospital about what transportation services they offer), if this is where his future follow up appointments are going to be at? And, there are transportation services that may be provided through your dad's health plan. Who is covering cost of the surgery? You want to talk to them about the need for ongoing transportation services, see if that is a benefit your dad qualifies for.
The VA does offer transportation services to and from VA-only appointments in some locations if the patient cannot walk a certain distance. I looked into it for my father and you pretty much have to be wheelchair bound in order to qualify... but... a local VA social worker might have suggestions for you.
If your father isn't getting his care through the VA medical system, they wouldn't be involved in helping arrange his transportation to other medical appointments.