My character is a pure mage. There are a number of strategies you can use: Currently I basically use a combination of Alteration/Conjuration/Destruction/Healing depending on # of enemies, MP, etc.
For example, I worked to have my descruction skill have the "Impact" perk, which gives dual wielding destruction spells stagger the opponent. Combined with firebolt / ice bolt, this is particularly effective. I've killed a dragon without getting harmed, standing 10 feet away simply by casting this over and over (and over) again. If you misfire though, make sure your healing is up to the task :).
However, another favorite tactic is to summon your strongest Conjured person (currently I have the dremora lord...holy cow that is one awesome summon), cast Oakflesh, and stand back and relax.
Along the same lines, you could probably also build up Illusion and make the enemies fight each other before they turn on you. That way, they're almost totally dead by the time they die.
Personally,I found it a mistake to put points into Mage Armor perk because I wear the Morokei dragon preist mask. Since this has 6 armor, it kills the mage armor perk. But for a mage, +100% magicka regeneration is worth the sacrifice.
In all, there are several strategies depending on which magic you want to focus on.