Hospitals are used to having people nap there while they wait to visit with loved ones, so you probably won't get bothered. Hospital furniture really varies from area to area so look around for the best place to crash. You might want to stow your gear somewhere by the way. Lots of travel gear might look a little weird to security. If you have transportation, try to leave your bags in the trunk.
Hospitals are usually pretty safe for that.
The parking lots are pretty cheap too. Get your sticker validated at the information desk and you often pay a lower fee. I had a Hertz double upgrade, for which they gave me a Lincoln Town Car. I arrived at the Westin only to find that they did not have a room for me and the entire town was booked solid. So, I told the desk clerk that I needed a couple of blankets and pillows and proceeded to sleep in the back seat of the Lincoln on the street in front of the hotel.