My girlfriend came along, she wanted to be there for an important time in my life. She just hung out in the school while I interviewed. Staff were extremely nice to her, joked around with her, and the dean talked to her for a while. Afterward we explored the area. Also, I was the only interviewee that day and didn't get a tour or anything extra, just about an hour of interviews.
I attended the open house at NYCPM. Most students came alone, but a few did bring a parent. These students with parents seemed to be in early college, probably not applying yet. To me, bringing a parent makes you seem less independent.