The purple site is definitely an option, but if you do that, I think you should put the city one square to the north, like I said during my turn. With that in mind, however, I still think the location next to the copper is better. We get the copper and also take it away from Hammurai, most likely crippling his military for a while. Furthermore, with that city in place, I think Hammurabi will attempt to expand in our direction much later. And if he expands anyway, that city may become a prime location for a culture bomb.
Also, if we hurry and put our third city next to those gems, we can close down our side of the continent to the rest of the civs. However, if we do that, we should prepare to play a more aggressive game, and start setting up proper defenses for those two cities.
Checking the last map, the following is a good place for that gem city:
The line above is the fat cross border for the copper city. With the two cities at 100 culture, which is easy with the creative trait, and the help of that mountain, we can block the passage towards our side of the continent.
And of course that also seems like another great food location for a city. Cows, corn, bananas, and a flood plain.