With 'on the night of', I would normally expect to see a specific date, for example: on the night of (Friday,) December 20, 2013, and not just 'Friday'. 'on Friday night' is infinitely better here -- at least in my opinion. You could also leave out the preposition.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Laborious"We will have a party on the night of Friday the 1st of January".Use this only in limited cases: