The level to which one is committed to in Dante's Hell is based upon the character of the person and how they lived their life. based upon the characteristics of Gilgamesh, he could be placed in many different levels.
First, Gilgamesh could be placed in either Dante's Fifth Level of Hell or Seventh Level of Hell. In the forest journey, Gilgamesh is faced with making a decision about ending Humbaba's life. Although Humbaba pleads with Gilgamesh, Gilgamesh refuses to hear his pleas and takes the head of the giant. Based upon these actions, Gilgamesh could be "sentenced" to either the fifth level (belonging to the wrathful and gloomy) or the seventh level (belonging to the violent).
Another level of Dante's Hell which one could place Gilgamesh into is Level Six (heretics). Depending upon ones own religious theology, the fact that Gilgamesh does not believe in God could insure his fate of spending his afterlife in the level deemed for the unbeliever.