Some suggestions:
Not all volunteering needs to be in a hospital. Think hospice, Planned Parenthood, nursing homes, rehab facilities, crisis hotlines, camps for sick children, or clinics.
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, the dying, 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.
Service need not be "unique"; it can be anything that helps people unable to help themselves and that is outside of a patient-care setting.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. The key thing is service to others less fortunate than you.
Examples include: Habitat for Humanity, Ronald McDonald House, 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 literacy or ESL to adults at a community center, Big Brothers/Big Sisters, Meals on Wheels, mentoring immigrant/refugee adults, being a friendly visitor to shut-ins, adaptive sports program coach or Special Olympics.