I agree with everyone on checking with the Wellness director. Could be she would love someone with your experience to help her out.

We have a cycling club at my office. We have a group email address to which you have to request to be added. Rides are announced and people say whether or not they are able to come. It's pretty informal, but it is a lot of fun.

I was thinking that an easy "challenge" to do would be a "step challenge" - with cheap pedometers. People in hospitals walk a lot - it may be very encouraging to see how many steps they are actually taking.