Connor returns to this dimension after finding a portal simply because of knowing where to look. He comes back after 16 years in Quor-Toth because he wants to see his father, his real father - Angel. His curiosity about him and his thirst for knowledge and interest drive him to find a way back to earth, and he does.
Of course as a result of everything Holtz taught him, with the interest comes the passionate hatred for Angel. As soon as he breaks through the portal and lands on the floor of the Hyperion, he aims a strange-looking self made weapon at Angel's chest and with the words 'Hi, dad', fires 3 stakes at him, 12 of which he ducks while the third one impales his shoulder.
After a swift battle with his father, who is understandably too shocked to actually *fight* and his friends, Connor runs out of the hotel into the day, almost causing Angel to fry himself in the sun by running after him. Luckily, Gunn and Groo pull him back in time.
Connor doesn't stop to bother and adjust to the new-found home, but instead he only uses what he can to fit his purposes, which are currently revolve around transportation - he doesn't have a specific purpose, he's mostly just lost. Also, it's obvious the meeting with his father didn't leave him as nonchalant and indifferent as he thought it would.
On his first day on earth, he manages to leave a well-respected trail of disorder and even violence behind him (bringing into action the habit of collecting trophies - in this case, cutting off a drug-dealer's ear after winning a fight with him and saving the 'damsel in distress'.
He is revealed to be a very smart and intelligent boy, but though he seems to be strong and impassible, he's not. Inside, under all the layers of defense, he's still a lost and lonely child. He's not stupid, but still naive in the ways of this world. It's clear he never had friends in the Hell dimension and the only girl he befriended here with died from overdose. It confuses him and briefly reveals a deeply concealed, more human side of him. However, the way he chooses to 'solve the problem' is not the way of this world, and clearly, he doesn't even know he's fighting the wrong battle. Luckily, Angel finds him in time and saves him, not only from certain death (he isn't exactly familiar with guns and rifles…), when he takes a bullet for him.
In the end of his first day back in this dimension, Connor (now Steven…) shares a brief moment of almost closure with his new found father. But again, he struggles to trust, struggles to let his emotions take over, struggles through hatred. Angel realized he can't push and his son has to make his own choices and he lets him - he promises him he's always welcomed to come home and Connor says he knows. But for now, he still walks away.