Should I choose the schools that I apply to, or should I ask my advisors to do that for me?
Fortunately, this isn't an either-or proposition!  I agree with your assessment that you shouldn't come to your advisors empty-handed and ask for some schools to apply to.  However, it would be perfectly reasonable for you come to them with a couple schools you like - probably spread out by competitiveness and such - and maybe some guidelines for what you want to focus on and where you would be willing to move to.
Ask their opinions on the schools you picked, and ask them if they have some others they would recommend, based on what they know about you.