To give a bit more detail to the previous answer, Montag runs there because he is fed up with his society, confused, and needing answers. It hasn't been too long since Captain Beatty invaded his home and gave him the entire history of their society, explaining the reasons why they burn books, and why people are so busy and violent. This gives Montag a lot to think about, but he really has no experience thinking things through; it befuddles him. Then, he has tried-and failed miserably-to bring Mildred along with him on his journey of knowledge in reading books. Her lack of cooperation and her frustration with the entire experience leaves him feeling even more alone hin his struggle. If she won't try to understand with him, who will? What pushes him out the door in the first place is her friends; he quotes poetry at them and they end up sobbing with misery, and storming out of his house, angry at the "hurting words". He runs out onto the subway, and is trying to memorize some scripture, but the persistent "Denham's Dentrifice" commercial keeps playing on the subway, blocking out his thoughts. Pushed over the edge by the realization that his society was designed to keep him from thinking at all for himself, and to keep him busily miserable, he goes to Faber's house. He feels Faber-who he barely knows-can somehow sort all of this out for him, help him to think it through, give him answers, and help him to not feel so alone.
Montag run to Faber's house instinctively (see page 124).