When negotiating the price of a new car, make it clear to the salesperson that you know what the car is worth, have already been on a test drive. Know what accessories you are looking for. The person selling the car needs to know you won't settle.
You can negotiate elsewhere if the current dealership is unwilling to change the price of the new car. Make it clear that you are more than willing to do this. Don't negotiate the monthly payments, but focus on the full purchase price of the vehicle. Negotiating monthly payments gets tricky, since it can greatly affect the actual purchase price of the vehicle.