Well, even pure mages can handle just about any baddie in the game at any level, depending on how you manage your spells. At levels above 15 or so it's quite necessary to start stacking up spell effects. I've found that a weakness to magic 100% for 5 seconds, followed by weakness 100% for 10 seconds, followed by weakness to element 100% for 15 seconds works nicely.
Right after those three, fire off a spell that does elemental damage for 2 or 3 seconds. Block, then fire again when the first one wears off. It will only take a few shots to bring down just about anyone.
You'll also be interested in getting your conjuration skill up to 100 so that you can summon the grand creatures. With them at your side to soak up some damage, you can even manage several baddies at once.
I usually carry a supply of welkynd stones when I play mages, because I like to have instant magicka recharges when things get tense.
Lastly, sigil stones are your friend. A few fortify magicka sigil stones can really work wonders for a pure mage.
(Other good ones are fortify endurance, and any of the elemental shield sigil stones).
Remember not to use armor or robes! Just enchant regular clothing with elemental shield from sigil stones, and your magic effectiveness will stay at 100 and you'll be better protected than any warrior.
Good luck!