I have had hotels check me in early when I arrived at the hotel at 8-9 am after a red eye flight.

However when I have a late arriving flight around midnight or later and plan to arrive at the hotel by 1-2am, I book the night before so I can get to the hotel and sleep.

Also when I have a late departing flight after midnight, I have often paid for an extra night and check out around 10-11pm.