Just a couple of thoughts. CarMaxx was mentioned above. The advantage for using them (I’ve used them twice) is you’ll get a firm offer that is good for 7 days. The offer is typically lower than what you’d get if you sold it yourself but higher than the trade in offer the dealer will give you.
The other thing is when you use sites such as True Car you’ll get an “average” price that is lower than the MSRP (for my Jeep it was about $4,000.00 lower). With that, many dealers are associated with True Car and will, by the terms of their relationship with True Car, sell you the car you want at the True Car price. In my case, that ended any haggling.
So considering both items above you can get a decent price for your current car plus a decent price on a new car, all without any haggling at all. Good hunting!