I thought that the touch magic in oblivion was kinda bad, as even the ranged was. But the ranged was improved vastly, and so could the touch system from oblivion. Instead of a "flaming touch," i thought maybe you could add it as a added magic bonus to your unarmed combat. It would slowly take away at your magicka pool and add the corresponding effect and damage bonus. Doing the same (if not more) damage as the ranged spell. I honestly get a bit tired of using the ranged magic when i get super close to my enemy.

It sounds like you are describing something similar to Flame Cloak. You use up big lump of magicka to cast it, but it lasts pretty long and damages everyone in melee range.

This. <3 flame cloak.

Indeed the typical touch spell has been removed. There are close range destruction spells in the game though. The cloack spells as mentioned above. And Flames, Frostbite and Sparks. For low level.
For high level destruction magic, Wall of Frost/Flames/Storms.