This is one of my favorite places to visit in SF, although I haven't been in about 3 years. When I went, it was free & I wasn't aware of it being a part of any museum. It's off on it's own, and it's best to get there early in the am - you'll have the place to yourself. Once there, it's really peaceful. If you're already in the area, I recommend it!
This location is also rumored to be haunted. This year & last year the Carnegie had a paranormal group tour. Hopefully they bring it back next year!
The Clark Center is going to close the summer of 2015. If you haven't made your way, you should before they close their doors forever!