I'd put a shoggoth in the cellar of the boiler room, but that's just me. It might also be a good area for longer-term storage, both for various supplies (you probably have things like paint, that aren't called for that often, as well as surplus of things bought in bulk that you don't want clogging up the smaller handy storage areas) and older records that you don't need to reference, but might need to hold for some time for legal reasons.

Perhaps one of the smaller rooms might hold a small lending library for use of patients (and possibly staff as well)?