What do I do here? You're in a hospital. I'm wearing a doctor's coat. I'm covered with blood. There are sharp, pointy things lying all around. Either I'm a successful killer or a fair doctor. Take your pick.
Holliday is a wizened old man wearing a doctor's coat. Born in Broken Hills in 2170, he met his wife while wandering the wastes. After she died he studied medicine in San Francisco, under the tutelage of Dr. Fung. Now, aged 70, he is Broken Hills' doctor.
Talking to Doc Holliday and listening to the story of his life will earn free healing from him (for Chosen One and his party) and also yield the fact that he knows Dr. Fung in San Francisco; allowing the Chosen One to have Dr Fung put Chip's spleen back in for free.
You can also get free healing if you ask what he does and banter a little, but you can only do that once, whereas you can get him to talk about his life over and over again. If for some reason you pay for healing he'll charge between $50 and $300 for each person in your party.
He sells stimpaks and other items and takes only half the price if you ask him to trade instead of hitting the barter button.