Our local Bon Secours Hospitals have a website and an area you can click on to send an email greeting to a patient. The email goes to the Volunteer Office, where they print it on a colorful paper and deliver to the patient.
This page contains the following solutions.
When I send get well cards to friends in the hospital, I use their home address as the return in case my card should get there after their release. This way, it still makes it to them without anyone having to look it up.