Paris is a good city to live?  Paris is a good city to live in?

The second one is correct, although it would be better to say "Paris is a good city in which to live".

→ B ... From me ¯\_(ツ)_/¯

Technically, you do not end a sentence with a preposition so you would say, "Paris is a good city in which to live."  But no one actually speaks that way.  The most natural way to say it would be, "Paris is a good city to live in".

A) is correct. You aren't supposed to end a sentence with a preposition. However, most Americans would use B) when they are speaking. I don't know about the British, they tend to follow the rules a bit more.

Most people would go with B. Definitely not A. 

(Paris is a good place to live, would be OK though, don't ask me why)

There is a tradition (rather than a hard and fast rule) of avoiding using a preposition to end a sentence with. But most people don't worry. The way around this: Paris is a good city in which to live. (But as Churchill said, this is the kind of English up with which I will not put)