60 is probably ok, but would you be happy having a relative fly with instructor approaching 80, no matter how spritely they may be.
Presumably you're worried about sudden heart attacks or similar? These can happen at any age. Do you have any evidence that they're more likely in someone of nearly 80 with a good health record, than someone younger? Remember, your 80 year old will have had a Class 1 medical within the last 6 months; your younger instructor won't.
Personally I'd rather send up my relative with the 80 year old with zillions of flying hours who can probably cope with practically any flying emergency, than the 200 hour 20 year old who possibly can't.
And I suspect sudden and unexpected aircraft failures are more common than sudden and unexpected heart failures. Anyone have the figures?