I just worked out my own answer for the mileage of an electric car on the moon.
I drive a Nissan Leaf. Using a spreadsheet I just wrote, and plugging in the best numbers I could find for the Leaf's usable battery capacity, drag, efficiency and overhead power, it gives me an estimated range-per-charge at 65 mph of 77 miles. The actual figure varies due to many factors, but this is pretty close.
Simply setting air density to 0 and the gravity to 1.622 m/s2 increases the range per charge at 65 mph to 888 miles. Not bad at all...
On earth, in air, range drops substantially at higher speed because aerodynamic drag force increases with the square of the velocity. Rolling resistance is constant with velocity, but varies directly with vehicle weight. So on the moon, aerodynamic drag goes away and rolling resistance drops to 1/6 of its earth value. Range actually increases with speed because the car's own overhead consumes more energy when the car is driven for a longer time.
This does assume paved roads...