If you were moving into the city for a few years and do not need a car which you are still making payments on - can you drop the insurance policy and continue to make payments on the car?

Typically, (depending upon your state) if you wish for a vehicle to NOT be insured any longer, you would need to turn in the license plate before being able to discontinue the insurance. BUT this depends upon your state. Contact your State's Dept of Public Safety or the equivalent.