For me, what I focused on with my Mage is:
Conjuration (Primary)
Illusion (Primary)
Enchanting (Secondary)
Restoration (Secondary)
Destruction (I don't bother with it)
Alteration (I don't bother with it)
Conjuration: If you're going to use bound weapons this is a must. I go this route early on. Simply because each summon is suited for one purpose or another. If you master Conjuration, you don't need to bother with Destruction or Alteration.
I. Flame Atronach/Boneman/Mistman/Storm Atronach if I need ranged support. A mage or archer dead thrall work just as well.
II. Frost Atronach/Dremora Lord/Wrathman are essentially your tanks, who needs added protection if they distract your enemies? The Frost Atronachs and Wrathman are more tanks while Dremora Lords can suck up damage, but deal extreme amounts of it and are a little squishy as well. You can simply get a melee thrall such as a bandit chief who can use a bow if needed to achieve the same effects.
I can't stress how useful Conjuration is, you can summon any ally you need for whatever the situation is: a Dragon? How using a Storm Atronach to ground it and summon Dremora Lords to finish it off. In a Draugr crypt? Summon your DL's and watch them go to town.
Illusion: This magic is similar to Conjuration. You can stop from being attacked, provoke enemies into attacking each other without being harmed yourself, cause enemies to flee in terror into other potential threats (e.g. a trap) or to give yourself some breathing room.
Enchanting can benefit a robed mage as well (if you want stay with robes), simply enchant a pair of gloves, boots, circlet, ring, and amulet and you don't have to sacrifice the Mage Armor Perk.
Restoration: Self explanatory.
Alteration: I don't use this, only because my summons soak up damage for me, if I'm facing a mage I have my wards.
Destruction: I do love destruction magic, don't get me wrong. The impact perk is wonderful, I just prefer to watch my minions slaughter everything. You might want to use destruction to deal damage primarily (everyone has their preferences).
I'm sorry for having so much typed up, (I get lost sometimes discussing a game) I hope this helps!