Let's think
the hospital scenario through given what we've seen in We're Alive.
During Phase One of a zombie apocalypse you can expect the hospitals to get over run quickly and early. No matter how, or where the outbreak occurs, some of the infected are going to end up being transported to the hospital, where they are going to turn and spread the infection. The first wave of zombies, whether they come in through the doors or they come out of the emergency room,
will over run the hospital and in short order it is going to be picked clean of human prey. The key to survival during this phase is to find a good place to hide and secure yourself. I'd suggest locking yourself in the most secure room you can find (radiology labs, store rooms, etc.) and douse the approaches with alcohol to hide your scent.
In Phase Two you can expect most of the zombies to leave in search of
places where there is still prey. We saw this We're Alive at
The Tower, and
The Other Tower, where all but a handful of zombie hangers-on were gone by the time survivors searched the locations. Even Cain Memorial Hospital seemed to be occupied by just a handful of lurkers and malingerers up to the point that the zombie army arrived, presumably from the Stadium. This would be the time to search the hospital to gather supplies, look for other survivors and make your plans. Just be sure to arm yourself to deal with the lurkers!