OP how did you get around when you were a teen?
Like PP said, carpool, older kid who lives nearby, bus service, bike/walk if possible. There are many options and none of them involve hiring a nanny to transport a high school kid.
I don't recall having to pay anyone more than $5-10 a week for gas before I could drive and I made it everywhere I needed to be (To and from school and various sports/clubs/theater activities, etc.).
Maybe just ask your kid what he would like to do...