Junglers have the most strategic sway over the game due to their ability to roam and affect the map from the start of the game.
You might like
Elise (jungle) due to her larger number of spells and utility.
Maokai (jungle/top/support) has to plan ahead with his ultimate now to use it well.
Gangplank (usually a solo laner) has interesting capabilities with his barrels and ultimate.
Xayah (bot) has some strategic mini-games with how she places her feathers.
Orianna (mid) has strategic gameplay with her ball.
Taric (support/top) now uses his abilities from both himself and an ally, and he has some delays that require planning ahead but that reward you well.
Lulu (support) has a number of strategic choices she can make with her kit and her gameplay can be fairly complex.
I'll think of more if you like, but it'll have to be after I'm off work. I did this on my break.