Not all volunteering needs to be in a hospital. Think hospice, Planned Parenthood, Ronald McDonald House, nursing homes, rehab facilities, crisis hotlines, camps for sick children, or clinics.
Service need not be "unique". If you can alleviate suffering in your community through service to the poor, homeless, illiterate, fatherless, etc, you are meeting an otherwise unmet need and learning more about the lives of the people (or types of people) who will someday be your patients. Check out your local houses of worship for volunteer opportunities.
Examples include: Habitat for Humanity, Humane Society, crisis hotlines, soup kitchen, food pantry, homeless or women’s shelter, after-school tutoring for students or coaching a sport in a poor school district, teaching ESL to adults at a community center, Big Brothers/Big Sisters, or Meals on Wheels.
Some types of volunteer activities are more appealing than others. Volunteering in a nice suburban hospital is all very well and good and all, but doesn't show that you're willing to dig in and get your hands dirty in the same way that working with the developmentally disabled (or homeless or Alzheimers or mentally ill or elderly or ESL or domestic, rural impoverished) does. The uncomfortable situations are the ones that really demonstrate your altruism and get you 'brownie points'. Plus, they frankly teach you more -- they develop your compassion and humanity in ways comfortable situations can't.