You may stumble upon a random NPC vomiting at many points during the game, but the best place to find one for sure is near the pier in Oakland, here:
Once you spawn here, at any time of the day, just run up and down the pier looking for someone who is obviously drunk and walking around. Follow them around for a few moments until they begin vomiting, and quickly take out your camera to snap a picture. If you are following someone and they are taking too long to vomit, try to find someone else. At this location near the pier you should be able to find someone vomiting every few minutes.
Solution by Maka91