According to my late mother's notes, Notre Dame Institute was in the former O'Connor Mansion at Second & Reed streets in downtown San Jose. The building is still there, now part of Notre Dame High School. You can google the high school and see photos, although there's no mention of the former orphanage.
Mount St. Joseph was in San Francisco and operated as an orphanage until about the 1970s. There's quite a bit of info about it on-line, including message boards where former residents try to find childhood friends.