If it's used to indicate the end of the day, such as the end of a time range within that day, use 24:00.
Anywhere else, use 0:00.
For example, if you want to say "free parking between 10 pm and midnight": 22:00 - 24:00
If you want to say "free parking from midnight to 3 am": 00:00 - 03:00
I hear in Japan train schedules actually use (or used?) numbers higher than 24 for the edge case of needing to indicate "3 am of the next day", e.g. 22:00 - 27:00, but I've never seen that elsewhere. In Germany that would simply be "22:00 - 03:00" with the date change implied (for timespans equal to or larger than 24 hours you would need to indicate the dates in question anyway, so it's not ambiguous).
In short: "Friday, 24:00" is equivalent to "Saturday, 00:00" but implies you're talking about something that happens on Friday (such as a deadline ending "Friday night").