President and Vice President from the same state?

[Nym90]

So what would happen if Bloomberg/Giuliani were to win NY?

Bloomberg isn't a Republican anymore, so you can count out any chance of those two being on a ticket together.

But hypothetically, the electors from NY would be prohibited to vote for a President and Vice President from NY.

One of the two could call another State "home"
ie Dick Chaney goes to Wyoming

...and they would. However, they'd have to do that before the election.

The NY electors, in your scenario, would just vote for some counting candidate for VP. Which gets interesting if that means Bloomberg's election goes to the Senate.

Actually half of the electors could vote for Guiliani and someone else and the other half could vote for Bloomberg and someone else; even if the election is close, this might be sufficient to get both of them to 270 electoral votes. If this would result in neither getting to 270, however, then they'd need to vote for the Presidential nominee to at least ensure his election, and take their chances in the Senate with the VP race.

But yeah, actually they'd just make sure that the VP candidate took up legal residency in New Jersey or some such.