Your best bet, financially, would be to sell the current SUV outright. You can find values on a number of web sites including NADA, Edmunds, Truecar and others. A couple of national resellers of used vehicles (Carmax is probably the best known) may buy yours outright but I cannot say you will get a better deal with them.
If your current SUV is very low mileage and in showroom condition you might get a better trade-in but it will never be as good as selling to a private party. If you go this route establish with the dealer the trade-in value of your vehicle and then bargain with them on the cost of the replacement. If you try to combine these two negotiations your chances of getting screwed are high.
Most new car dealers these days are either chains or they are owned by national companies. They have every resource, including financing, to sell their best deal. Chances are, if you threaten to walk across the street from Nissan to Toyota the parent company will own both dealerships so they really don't care whether you walk or not. Have any financing already set up with your bank.
If you negotiate with any dealer during the last few days of the month (or a quarter) but not on busy days like Saturday they will usually be in a better position to offer a better deal since they may need to make quotas from the manufacturer or have inventory taxes coming up. Asking for an Internet salesman may also get a better offer (not guaranteed) and buying from lot inventory almost always makes sense from a financial point of view.
Whatever you do, do NOT expose your hand ("I REALLY LIKE THIS CAR") or otherwise indicate that you have fallen in love with a particular car prior to financial negotiation. Salesmen will milk your emotions without mercy. Do not be in a hurry to close the deal. Recognize you may have to deal for hours or sometimes days to get the deal you want. Don't allow the dealership to pad the vehicle with all sorts of BS extras like glass VIN etching, undercoat, paint and fabric protection etc. And the most important rule of all:
BE PREPARED TO WALK AWAY IF THE DEAL ISN'T IN YOUR BEST INTEREST
If they want your business bad enough they will call you back.
