At 60 I hadn't even started riding yet so nothing for you to worry about. Not until I ran 1 too many marathons and needed a hip replacement did I turn to cycling.
Now I ride about 3k miles a year and really enjoy it. Hills are my favorite and we have plenty of those in New England.
67 now and exited about riding the New England Classic "Tour de Cure" again to benefit the American Diabetes Association. 7 days and about 28k feet of climbing what fun!