You should take that website as any other and start by asking the question "what do people expect to see in this website?".
I think there will be two different kinds of use cases. The most common one is someone that needs to get some information and then he/she leaves. This can be a phone number or a schedule for example.
Other people might want to find information about the hospital, its history and traditions. I feel that this will be a lesser use-case.
Stuff to avoid is information that is not relevant to the hospital or does not contain a good time-to-value proposition (you know, too-long-didnot-read TLDR). For example, I find the the photo gallery quite awkward and not really associated to the hospital. If those are part of hospital events then they should be on an events page.