@BJ: "Llevar" has a passive notion but you want to express that an action is being performed by your car, so it can't be used for this example.
If you say "mi carro tiene/lleva ___ millas por galón", you're saying how much it has spent.
You could say "mi coche lleva trescientos mil kilómetros recorridos" or "mi carro tiene 4,000 galones de gasolina consumidos", both of which are talking about what your car has "done".
But if you want to talk about the performance you get from your car, an active verb (like those Chileno suggested) must be used.
Mi carro rinde/da ___ millas por galón.