Sister Christina is correct -- there really is nothing in their archives that would be of any help to family historians. The published list is the only "inventory" of the students pre-1880, and none of the students post-1880 have been compiled as of yet. Hence my problem with identifying parents of the students. As far as what else to see at the convent, do visit the museum and ask to see the chapel; it was built as a "hidden" structure. There is nothing viewed from the outside that suggests there is a church there. Have you been to York before? If not, I can certainly point you to places the Goodman girls would have visited.
Regarding the Leeds Barracks, I believe they are actually called Carlton Barracks (they're just in Leeds and so referred to as the Leeds Barracks). I haven't been, but if they are one in the same, then they are located on the north side of the city near the university district, just off Clay Pit Lane and the Inner Ring Road. You'll have to check with someone in Leeds to find out for sure.
One question for you before you go -- do you have a full name for the wife of Stephen A Goodman?