Probably just after 10
The Hollywood Burbank airport is open 5:30 AM to 10:00 PM, but some ticket counters close before 10:00 PM, and most restaurants close before 9:00 PM. Rental cars may not be open after 9:00, so be sure to reserve online and check the hours. The Metro is rather scarce after 9:00 PM as well, but you should check hours as they add more lines and extend hours on the Metro over the next couple years.
The business office is only open from 8:00am to 4:30pm, but the passenger concourses are open for all scheduled flights. So, if you have a flight, the airport should be open early enough to comply with the "recommended" pre-flight arrival times. As mentioned above, concessions generally close by 10:00pm.
Noise levels are restricted nightly
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