The word vice has some moral connotations, suggesting that this bad habit is due to some kind of flaw or weakness in a person. However, it is often used in a humorous way. For example, I say that my vices are coffee and chocolate.
Guilty Pleasure
A similar term that we could use is guilty pleasure, to describe the things we enjoy, but that we feel some kind of shame or embarrassed about, because of thinking we’ll be judged by others.
Her guilty pleasure is eating a full tub of chocolate ice cream every Friday night!