In many hospitals, you will find these options quite limited, if even offered at all. Your best bet would be a major teaching facility. But I doubt if you will be able to find many shadowing opportunities. Or you will not get a very complete view.
Per HIPAA regulations, it is rare for a nonemployee/nonhealthcare worker to be permitted to shadow, due to potential privacy problems. Currently, hospitals are jumping through major hoops, to prevent any unessential dissemination of patient info...even the most benign data. Having an "outsider" in any position where they can obtain that data is banned in most places. And "shadowing" a nurse definitely falls into that area. There would be absolutely no way to provide you with a complete overview of a nurses job, without you having some "protected" information.
As an example, as a licensed RN, I applied to a facility for two positions, one of which was home health. I was offered the opportunity to "shadow", so that I could see what the job entails. I said yes, but the offer for a shadowing got retracted, by legal department, due to privacy issues and possible liability. This was despite the fact that I as an RN would be barred from dessiminating private data, and held my own liability insurance.
I could imagine that it is more difficult for nonlicensed personnel.