Probably not a good idea to put your employer's information on your cards. If your position required business cards, your hospital would make them up for you. If a supervisor at your job saw personal business cards made up with your name and the hospital's name, they might not like it.
That said, and the reason why this thread caught my eye, is because I do have cards with my name, title (RN, BSN), cell phone, and email address on them. When I had a stable place to live I had my PO Box number on it. I give them out if somebody asks for my phone number or email. People always comment on them. In Victorian times it was customary to have "calling cards" to give out. I got the idea from RNs I used to work with, who had their own lactation consulting or doula or educational personal businesses. Once I become a lactation consultant, and / or CNM, I am certain to have cards made by my employer. But I might still have my personal cards with my upgraded credentials listed ... because they are personal, with my personal, not business, contact info on them. You can give them out if you're making contacts, schmoozing, applying for a job, &c.
I got my cards very inexpensively through www.vistaprints.com