I know people disagree with me, but as someone who has spent a significant portion of her life as a patient and inpatient, I strongly encourage you to actually do a job rather than just shadowing. Whether you volunteer or work for money, it is just more ethical. You learn the same things as you do just following around the doctors "shadowing" BUT you also learn the feeling of personal responsibility for and relationship with the patients. I particularly do not find it appropriate to shadow in pediatrics inpatient clinics for this reason.
I do not think it is the ideal situation for patients when there is a shadowing pre-med, b/c they can feel gawked at. Indeed, if you've ever been presented to a swarm of med students during rounds, even that is enough to make one feel like an object and not so kind towards the gawkers. Even though patients are often asked if it is ok for the shadower to observe, the doctor is in a position of authority, and I know many patients who have said "ok" b/c they felt uncomfortable telling the doctor "no," particularly if there is an additional disparity in authority such as a major age difference b/t the dr. and patient as in peds.
I find GI incredible for exposure b/c it is far more interesting than I believe people expect, and I think the interaction with patients is quite unique. Individuals with severe GI issues find their illness taboo to discuss--it's not like having breast cancer--they're often embarrassed. In the GI office, you can feel just how relieving it is for many of them to be able to openly discuss their illness and finally be able to receive advice. For some of them, when that exam room door is closed, it is the only time they can really find that openness and comfort. Plus, GI has procedural and surgical aspects...not all "personal" fields will give you quite the exposure to procedures.