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I'm not sure which way to say something like exit/leave/depart/get off/escape is most appropriate when the thing I want to get off is the system of expressways in Tokyo called the Shuto 首都高.
I'm not sure that any of these would be right:
You can use 降りる. User @Chocolate is also fond of 出る
高速を降りる
高速を出る
You can use these in the same way to express your idea of getting off of one form of expressway onto another.
首都高を降りて高速(or whatever)に入る・乗る
Just to address your original guesses:
出発する is to depart, as in the place of origin.
下車する is to get out of a car/vehicle.
残す is to leave something in the same way that you might leave food uneaten.
終了 is when something finishes.
"get off the Shuto onto a "proper" expressway out of Tokyo, like the 中央道."
In this case, I'd also say:
首都高を抜けて中央道に入る drive out of/through Shutokou and continue onto Chuoudou
