What was Mike's reason to move himself and the family back to New York? I know he sold all the casinos and made money for everyone in NYC. But why did he move back? Was it easier for him to pursue his legitimate business interests in New York? He claims he keeps getting pulled back in to mafia business, but he is the one that came back to NYC and stayed the boss of bosses of the commission.

Ace

Well, if he was really intent on going legit, then NYC was the best place to pursue that. His roots were there and it is the financial capital of the world. Also, in order to disengage from the underworld effectively, he would have to engage in some face to face conversations with his underworld colleages to make his point and they were primarily in and around NYC.

I agree with Olivant. Besides, given the negative associations many people (particularly powerful East Coast types) have for Nevada, it'd be hard for Michael to be regarded as a "legitimate financier" with a Tahoe address.

As for Michael being "pulled back" into the Mafia: He never left. Right near the beginning, Vincent says, "Zasa knows you're blocking him from rising in the Commission"--proving that Michael was still a member of the Commission, if not the chair. Later, in AC, we see him preside over a Commission meeting.