My apologies for the late reply, I feel there were some points missed that need to be addressed.
they get it back up too quickly though, and then your stuck just constantly breaking a ward and doing little to no damage.
As Ryusei said, they get their wards back up really quick. As soon as I try to fire again, they're already defending. I usually use the Dual Firebolt and then use Yol so I can damage them a bit.
That is why lightning is your friend. You charge the spell as they begin to stand and discharge the spell just prior to them casting their ward spells. Any other spell has a delay at reaching them and they inevitably protect themselves from your still travelling fireball. Another thing to consider is a fireball wastes a large percent of it's power by exploding in all directions, lightning hits with all it's power due to the conductivity of electricity.
Used correctly, and given the magicka reserves of a superior Altmer, you can kill even the mightiest of foes with a low level dual cast lightning bolt without taking any damage. Though it may take you some time.
Combine conjuration and destruction. Summon something and zap the enemy as they concentration on the summons. Also if playing a destruction mage focus on no more than about four skills five at most (e.g Destruction, Conjuration, Alteration(or LA) maybe sneak), aim to keep the world level less than 40 at full development.
Still I have been trying a Destruction, Alteration mage. The occasional sneak, and summons in boss fights. Works but making a full Destruction, Alteration, Conjuration mage seems more natural and is probably the most powerful purely mage build. Just remember to not employ any other skills except in exceptional situations.
I think Illusion probably weakens the build overall.
Good advice overall, but I strongly disagree with your views on Illusion. I think it is the most powerful school of them all, given the right circumstance of course.
Right off the bat you have (If you have the superior skills of an Altmer) Fury. It works on everything you are likely to encounter in groups at the early stages. Continue to improve it with perks and it is effective surprisingly longer than you would think. By the time it reaches the end of it's usefulness, you should be more than able to cast it's replacement, Frenzy.
Calm, Fear and Muffle and very good for crowd control and for surprising your foes. With no real skills in sneaking, I am able to walk right up to my enemies after calming them and dispatch them with a dagger, yes even an iron one. And simpletons that you cast fear on can clear a room of traps for you with no real effort on your part or alert you to wild animals if used outside. Should things go wrong, Muffle helps you make a quiet exit at speed and as a bonus doesn't trigger the automatic defences of Dwemer ruins when you pass them.
Once you have mastered the basic uses of the Illusion school, you will find the more powerful versions add to the complexity of the situations you can involve yourself in to the stage where as a true master of the art, I can walk through the most dangerous of situations without angering a single person or by getting them to dispatch themselves while you go about your business. It is very useful should you need to retrieve information quietly without making yourself new enemies should a disguise not suit your race. Some of you will understand what that means, some of you will not. I will not explain further.