Hilton properties are typically midnight (local hotel time) the day before arrival.

Many of the others are 4pm (local hotel time) 1 day prior to arrival.

It's always local hotel time and the cancellation policy may vary from hotel to hotel.

So, if you policy says 24 hours prior and it's a Hilton, it is midnight the day before arrival. If it says this and it's most other brands 4pm local hotel time is safe (since some are 6pm).

Very important to factor in 'local hotel time' when changing time zones.
And, I agree, you should always look at the specific policy stated on your email confirmation (never guess the time); sometimes it's the 4 or 6pm local hotel time the day of arrival (in which case, it will not state 24 hour cancellation policy).