I was going to suggest a nursing home as well. At least locally it's rather common for new graduate RNs, especially BSNs, to get managerial positions in nursing homes. If not managerial, then they're at least supervisory and seldom deal directly with patients.
Another mentioned something about home health. There seems to be a lot of turnover in that area locally. I'd suspect that because of that one could get a home health job and move into a supervisory or managerial position in a short amount of time.
I personally am interested in general administration. Nursing management (house supervisor, etc) doesn't have much of an appeal to me, but things such as finance, compliance, personnel, and so forth interest me. I've dealt with much of that in a previous government, although not healthcare, occupation. Supervising people isn't all it's cracked up to be. You have to understand that to do your job you're going to, at times, greatly offend some of your staff, but that's only one end of the spectrum. Some supervisors aren't comfortable with that. Confrontation isn't an issue for me. I liked supervising, but I really enjoyed organizational leadership, i.e. having vision and driving the organization towards a goal yielding improvement.