I wish you had a choice to choose where to volunteer at. Among the options you posted, a large hospital is definitely a better choice. But a volunteer position is never easy to have doing what you wish to do. But you will never know until you submit an application.
So, make a good resume and definitely submit it to the hospitals or clinics you are interested in. Maybe even call them or go there and ask to speak with the director of the department. It might be a long shot, but it doesn't hurt to go the extra mile, if this is something you really want to do and achieve.
I live in Houston, Texas, and I know a lot of the hospitals down here have a big volunteer department, so what you are seeking is very possible.
I wish you goodluck in your search and goodluck in school.
And if you have any specific problem with school and need help with school, just feel free to email me at email@example.com. I can help you sail through school very easily, if you are having any hard time with any class.