In my experience, Car Max low balls you by a lot. Every time without fail they offered me 3-5K less. Privately selling is a hassle and you have to pay taxes anyways so you're not entirely done.I have an appointment at the dealership in the morning. The sales manager really perked up when he learned it is Aleutian Silver.
Going to the dealership is best because they will offer you more due to the fact that they can sell the car, since it's their brand, and everything is worked out there. Just simplicity and better IMO. If you're already going to get rid of it and want better mileage, look into their trade-ins there. Maybe even a Tesla. Cheers!