After midnight when the metro stops, dolmuş minibuses still run from Ortaköy to Taksim and Beşiktaş. Around 41-42 TRY instead of 150+ for a taxi.

Look for the ones with Taksim or Beşiktaş written on the front. They get crowded with party-goers but it's part of the experience. Drivers are used to slightly drunk passengers and know all the shortcuts.