I shadowed at a rehab hospital during the week. Their main OT hours were from 8-4 M-F. However, I know they had Saturday OT hours as well. They had certain OT's who worked on Saturdays with patients who missed their weekly OT and had to make it up over the weekend. They were very strict with OT and PT hours. Patients had to get a certain number of rehab hours per week and if they didn't feel well/missed it due to dr appointment, they HAD to make it up on the weekends. So I would check with a rehab hospital. The place I went to was very flexible, you gave them your availability and they were able to match you with an OT/PT/Nurse to shadow. ALso, I was going to shadow at a children's rehab place but wound up not going because it didn't fit with my work schedule. Basically the hours were 2-8. She told me to come during those hours because that's when it was busiest because kids were getting out of school and could attend sessions after school hours.
Weekends will be hard to find a place, as they give most patients off on the weekends but I would check out rehab hospitals and pediatric OT.
I would also check out nursing homes, as they also do weekend therapy at times. (again, for people who miss therapy or need extra therapy).
Where are you from? If you are from my area I could help you out...