Probably not quite relevant to visitors of the glorious Minotaur Maze (R) that is the PAH, but there's a decently sized staff bike park downstairs in the VMO car park. I've been parking my bike there since I was a med student in '06; there's also some showers nearby too. For any staff member wanting to get access, see the security staff on ground floor for the combination.
Unfortunately since they expanded it to cover 4 car parking spaces couple of years back, security has been clamping down people parking their bikes outside of designated areas. They probably don't realise that visitors may, on occasion, feel like riding their bikes to visit their loved ones.