I love to cook or words to that effect. I've been doing it for years and really enjoy it. I wouldn't add anything about the hospital. After all, cooking is cooking no matter where it's done.
Honestly, I would play it up as much as you can. Tell them that you want to feel like you are making a difference in the lives of patients by giving the nutrition and sustenance that they need or something like that.
I'm applying for a job as a cook for a hospital, but I'm not sure how to answer this. I don't want a vague, " I like your services/products" or a "just be honest" type answer. I have 13 years of experience in the food service industry, if that helps.