It's hard to live without armor. If you must, make sure you have the mage armor perks, put your stat points into health, and use heavy damage to keep them at bay. I recommend the dual casting impact perk in destruction and self-enchanted gear (enchantment is the most powerful skill in the game and a must for a pure mage) that reduces destruction cost to 0. Level 75 destruction spells should overwhelm single targets, and level 50 destruction spells with impact can "stun lock" multiple targets. Kite melee enemies (run backward while using dual-cast destruction and they should never reach you), and use cover against ranged attacks, duck out and launch your attack and then duck back in behind cover again (fireball and ice storm will help if you have trouble hitting them - and remember lightning is instantaneous so it can't be dodged).
You'll be near-invincible at high levels like that (be sure to get elemental resistance on your gear as well, and use fortify enchantment potions to make it as high as you can), but the lower levels will still be tough. As others have said, tanks to absorb the damage while you zap the enemy can be a good idea - adding conjuration to your repertoire will make you very powerful, but a good follower can help you weather all but the most difficult situations (10 draugr stuck in a room with you). I recommend you avoid places like Dustman's Cairn (early Companions quest) and Dead Men's Respite (Bard College quest) until you're stronger.
Finally, alchemy is second only to enchantment in terms of power for those with no armor. It's worth looking into, though I'm on a no potion runthrough and I can't offer much advice (I guess restore health, restore magicka, elemental resistance for dragons and warlocks). Stealth can help a little, but magic makes loud noises and bright lights so it's of limited use. Illusion, if you want to be a "complete" mage, will save your life (especially with the perks). Just be prepared for some hit-and-run until you grow into a heavy mage.