I wouldnt, parents are just embarrasing
It depends how you think you parents will act- will they pass judgement and try to convince you to go to one place or will they let you make you own choice?
When I was going to uni open days I went to some on my own and some with my Mum.
I noticed that when I was alone I was more likely to engage in conversation with faculty members and ask questions about the course. But when I went with my Mum it was nice to have some company at lunch time and on the journey. It was good because my Mum isn't the type of parent to think I should be doing a particular course or going to a particular uni so she was just there as company and because she wanted to see what universities were like. Many people go with their parents and I think as long as you stick to making your own decisions (doesn't mean you have to agree or disagree with your parents, just do what feels right) then an opinion from your mum and/or dad can be useful