When laying out the board tiles Civilization V has an uncanny knack of placing the luxury resources exactly six tiles apart.
Should I drop one city in the exact middle between them and grow it to work both, or create two cities - one for each luxury?
Happiness is generally the key to how fast and how large you should expand. Almost every other statistic in the game is positively improved by more cities besides happiness. In most of the "average" difficulty settings I will tend to only place a new city where I can get a luxury resource I don't already have. I might consider a duplicate luxury resource, but only if I am certain I can trade it to a friendly civ rapidly after creating the city.
On a far below average difficulty, spam cities. Far above average, you've got to be very careful when expanding - the location should be very good and you should be prepared to build out quickly to keep your happiness in balance.
Don't neglect the other special (non-luxury) tiles - they can make a big difference if you can properly stack them to exploit buildings.
To demonstrate my strategy, here's a suggestion for your current situation, assuming average difficulty and no other modifiers (ie, Gandhi, certain wonders/policies, war, etc):
I'd suggest one city to the east of the gems. There's a lot of fish here in the water tiles, so I'd probably be tempted to place the city two tiles east of the gems. From this position, you get sheep, cows, horse, gems, and 2 fish resources. If you don't need the horses, you might consider the tile northeast of the sheep - this gives you river access for things like water wheel and hydroelectric power. This would be a good city for a stable.
For the second city, I'd suggest southwest of the marble. From here, you get marble, wheat, 1 of the 2 nearby stone, and 4 fish. That's probably about the best you can do resource-wise. The lighthouse will be super powerful in this city, and you won't go wrong with a stone works.
This is not a right or wrong question, rather about different opinions. There are so many other factors to consider here.
The only downside of two cities I can see here is that you have more unhappiness. But there are plenty of other resources to gather here, maybe even strategic resources that are not yet revealed. More cities also means more research, more units, and faster expansion of your borders.
So in my opinion, you should build two cities, except when you are playing India (higher unhappiness per city) or your happiness is very low and unlikely to rise soon.
As others have said, the key to growth in the short term is happiness. While this is important, it's also worth remembering that the key to sustaining your population in the long term is food.
Personally I would build cities in the middle of each of the luxery spawns so that over time they grow into the resources, while still having plenty of space in the late game to continue that growth without causing food shortages and starvation - which lead to negative growth as citizens begin to die.
In the case of your picture I would (roughly) layout my cities like this:
There are actually probably too many cities in this example but with this distribution you end up getting all of the luxery resources while still having plenty of space for growth as the game progresses.
Short term happiness does not equal long term growth.
