tl;dr parents are out busy, dad can't drive me, my sister says this is the time to be independent.
What's there to do at the mall? If it were me, I'd just go to gamestop or whatever. What would you do if you had a day free? I know a lot of tempers are around my age, and some even older.
Do what you like.
Don't go to the mall "just because" you have a day free if you don't need/want to go there.
You want to go to gamestop? then go. but don't force yourself to go if you prefer staying home.
But don't act like it's something exceptional, that you are doing in their back. It's not like you are chained home, and just sneak out when they can't watch you.
You are free to go to the mall whenever you want, not only when your parents are not here.
If I had a day free, I would stay at home and watch video/play/code/browse forums

Just do what you like.
I'm 35 and still at my parent's home. I have a job, a car, but no home (cause it's too expansive), but I don't go out when I don't work.
they tell me "go out, profit of the life !", but I am already profiting of my life by doing what I like. People think that profiting is "going outside, walking randomly without reason", for me it's doing what I like.
Of course, you could force yourself to go out, you are still young and probably still at school. Find some friends (boys or girls) to be with which share the same things you like or you'll end up alone.
Trust me, being alone later will be harder to find friends or a wife (if you want one), because everyone will already have their own life to manage full-time and they won't have time to spend with "making new encounter with a stranger" when they already have their own friends. (of course it will depend where you live/hang out)