....then play a mage that doesn't use any destruction spells.

Level 15, robe wearing mage, never cast a single destruction spell. Rely entirely on the other magic schools. I die a lot but its a blast. It forces you to maximise your use and knowledge of the other magic schools, everything is a running battle, you rely on the environment (running enemies into dungeon traps, places they struggle to get to you etc), using potions and shouts, keeping companions alive...etc. Highly recommended.