Any number of traits could be identified and described for the protagonist of Looking for Alaska.
Miles is introspective and a "thinker." His somewhat strange hobby/obsession with the last words of celebrities and historical figures is a little morbid, but reveals these traits. His ability to recite and apply those final words and sayings to the events of his own life reveals his intelligence as well.
Miles is also not materialistic in anyway. Life, for him, is not about the accumulation of wealth or things, but rather an adventure and a quest for the "Great Perhaps." He is an idealist.
Secretly, Miles desires to be a rebel. Although his outward behavior is often subdued and reserved, inside Miles wants to be free of societal conventions and restrictions. His attraction to Alaska is but one example of this trait. In many ways, Miles draws many connections to Holden Caulfield from The Catcher in the Rye in this regard.