"Paris is a nice city to raise children."  Is this sentence grammatically correct?

Here's the problem: native speakers are taught in school not to end sentences in a preposition, mostly to stop them from say "Where is he at?" But it's perfectly ok, and always has been, to end a sentence with a preposition. If you were doing formal academic writing, you would write "Paris is a nice city in which to raise children." But no native speaker would ever say that in conversation. They would say "Paris is a nice city to raise children in."  If you leave off the "in", it would be understood, but it's not really accurate. The city isn't raising the children. 

The correct sentence would be "Paris is a nice city in which to raise children."

Actually, in this instance, "in" is understood and, because of that, it doesn't need to be included. Also, if it were included, the sentence would end with "in" which is not good.

You bring up a valid point.

There are a few ways to address this. I offer some examples:

- Paris is a nice city in which to raise children.

- Paris is a nice city for raising children.

- Paris is a nice city for the raising of children.

Note that "nice" is perhaps not the best word choice (though grammatically it is fine). "Good" or "suitable" or something similar might be better.

Paris is a nice city in which to raise children.