That is unknown as of yet. Tyrion has a long journey ahead of him, and some of it is not going to be easy or fun. I believe he finds something near the end of book 5 that he has been searching for his entire life.
Well, it’s obvious he has been searching for someone to love him despite his dwarfness.
His character at first really turned me off, but he has grown on me and now he is my favorite character, along with Brienne of Tarth. Jaime is starting to grow on me too, I never thought that would ever happen!
Dany and Klal Drogo were also favorites.