At what point, after the events of GF II, does Michael decide to move The Family back to New York? Did he ever regain power in the city before handing it over to Zasa? I didn't like the Vegas setting for the Corleones, as the city is just so much more romantic a setting for gangsters. I understand that Vegas is just as notorious for mob activity, but New York is where it all started here in the states. Sorry, as a resident of the tri-state area, I'm just Partial to the "Big Apple".

There is what? A twenty year or so gap between the end of Part 2 and the beginning of Part 3?
I don't believe we are ever even given a clue as to when during that period Michael moved back to NYC.

But even while in Vegas during Part 2, I don't think he had given up his power in NY.

Remember, he tells Pentangelli at their vegas meeting "Your family is still Corleone".

Even with Zasa "in control" in NY, I suspect that Michael was still "The Boss", and while he may not have been taking an active role in NYC affairs, Zasa was still cutting him in on the action.

As plawrence said, we're never told when Michael moved back to NY. And, as he also said, Michael never let go of NY because he controlled Pentangeli and (presumably) Zasa.
I'm going to guess that, after Michael moved Klingman out of the Tropicala, he had sufficient legitimate operations in Nevada to move to the next phase of his "legitimization": laundering money for himself and his partners in the Commission. The fact that he was called before and accused by the Senate subcommittee also exposed his past and made him somewhat notorious even to the lax authorities in Nevada. True, Pentangeli renounced his affidavit and Michael wasn't charged with perjury, but I'm guessing that the publicity he generated would have made it hard for Michael to achieve more in Nevada. So, I'm guessing, not long after he whacked Fredo and Pentangeli, he moved back to NY and to a so-called "legitimate" life.
BTW: Michael's base was in Lake Tahoe, not Las Vegas.

As he writes to Mary and Tony, it has been several years since he moved back to NY. Since the movie takes pplace in 1979, that could mean the mid-70s or earlier.

When Michael "retired" from the street action of the Cosa Nostra, he turned the Family over to Zasa. But, he apparently was a member of the Commission, wealthy, respected, and obviously powerful since Altobello was intent on getting rid of him.

I don't think Mike turned the Family over to Zasa. Zasa had his own Family and Mike let him take Control of what used to be Corleone Family operations while the Corleone Family was heading towards the path of legitimacy. Pantangeli is a different matter because he was Mike's henchmen.