Myth: Coffee cures a hangover.
Fact: Coffee might wake you up as a regular stimulant, which you very will might need after a late night out. However, it does nothing to actually remove the alcohol still in your system.
Just to be clear, drinking coffee at the end of your night out will not reduce a hangover and will likely prevent some much needed sleep. Nor will drinking coffee when you first wake up reduce the amount of alcohol in your system. Coffee won't be the magic to sober you up.