If you have a specific geographic location in mind then search for all the job opportunities there and look at the hospitals tax exempt status. Or just tell one of the recruiters that keep blowing up your phone that you're only looking for employment at a 501c3 and have them do the work for you.
Two important questions you may want to ask yourself...
Is PSLF worth it?
Where I live, some people in private practice are making significantly more money than those employed by a non-profit hospital (hundreds of thousands of dollars in some cases). Depending on what year in residency you are, it may be hard to forecast what kind of income you could make in a private practice situation vs a hospital employed position after graduation, but if you got a job offer for $300k from a hospital but had the potential to make $500k+ in private practice, you might be better off in private practice when taking into account the entire length of your career.
Will it even be a viable option?
2017 will be the first year that people who have been on a PSLF plan will be eligible for forgiveness. I have no clue how many participants there are or how many are doctors/dentists, but I'd guess that when the public finds out that the federal government is forgiving some doctor's $300k in student loans even though he's making $3-400k/per year, there will be some outrage. I haven't read the fine print since I don't participate in the plan, but being that it's the government I'm betting they have the ability to change the eligibility requirements on-the-go and you might be out of luck.
