I know that St. Mungo's treats illness and injuries caused by magic. What about those injuries or illness that are not caused by magic? Do they go to a Muggle doctor or hospital for treatment? Example Dumbledore and Harry wear glasses where do they go have their eyes examined? I would think wizards/witches being part human would get Muggle related illnesses also.
They'd use basic magic to fix them. No long hospital stay would be necessary.
I pondered the issue of illness and disability very early in the creation of Harry's world. Did wizards catch colds? Could they cure illnesses that baffled Muggles? Were there disabled wizards? What were the limits of wizarding medicine, or could it fix anything?
I decided that, broadly speaking, wizards would have the power to correct or override 'mundane' nature, but not 'magical' nature. Therefore, a wizard could catch anything a Muggle might catch, but he could cure all of it; he would also comfortably survive a scorpion sting that might kill a Muggle, whereas he might die if bitten by a Venomous Tentacula. Similarly, bones broken in non-magical accidents such as falls or fist fights can be mended by magic, but the consequences of curses or backfiring magic could be serious, permanent or life-threatening. This is the reason that Gilderoy Lockhart, victim of his own mangled Memory Charm, has permanent amnesia, why the poor Longbottoms remain permanently damaged by magical torture, and why Mad-Eye Moody had to resort to a wooden leg and a magical eye when the originals were irreparably damaged in a wizards' battle; Luna Lovegood's mother, Pandora, died when one of her own experimental spells went wrong, and Bill Weasley is irreversibly scarred after his meeting with Fenrir Greyback.