I volunteer 6 hours a week at the local hospital (there are only two in our town).
I work in the emergency room, which is tons of fun. I get lots of patient interaction, nurse interaction and some doctor interaction, plus a chance to see all the "cool" stuff that comes into the hospital (which in all honesty isn't much--I'm in a podunk town, most of the more interesting stuff goes to the bigger city just down the road).
I take vitals of patients, have performed EKGs, hook patients up to monitors, help draw blood, and watch anything and everything I want to, as long as I have the doctor and/or nurses' permission.
I love it and that's why I volunteer six hours a week instead of 3 like I use to. Here are some hints:
Make sure you get into the area of the hospital you want to be in. Trust me, I was in a similar setting as you and I really didn't get all that much out of it. If your first choice is full go for a second or third. If you get stuck doing something you hate, look for a volunteer experience elsewhere.
Ask about what you can and cannot do while you are at the hospital. For example, the other hospital in town volunteers cannot perform vitals on patients at all, and barely get patient interaction other than when they are stocking their room. I was asked to suture a patient once, although I declined (second day at the ER and I didn't need to mess anything up). I know if i was in the other hospital I would be so bored there compared to what I do now.
If there is another hospital in town ask about their volunteer program.
Also, rather than volunteer you might ask to shadow a doctor around the hospital. There are a few people I know who do that instead of volunteering.
Hope this helps. As I've always been told, if you don't like doing it, then quit and find somethign else.