This place is open to the public so it's worth the trip because you're free to take photos as you walk along the grounds and take your time. I wish other locations were open to the public too! (see comments below) It's located at 45 Hospital Road.
Shutter Island and The Box were filmed here. This may sound weird but in addition to the old buildings, you can also find some interesting birds and bugs there - if you're into that sort of thing. I found the coolest beetle there.
The hospital was built in 1892 and is about 900 acres in size.

