The Emergency Room has valet until 6 or 7, I believe. Their security will also watch your car if you have to leave it up front, until you can go back to park it, given you might be visiting later than business hours. Even if you aren't going to ER, they will still let you park out front for a bit. (In case no valet anywhere.) The other sections basically follow business hours for valet, sometimes don't have people there until 8am, or have people leave valet station early (4pm or 5pm). Somedays, no valet at all. Just giving the realistic version here.
It is available from about 6am to 6pm from my recollection.
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