Whats the benefits of settling on stone?

[DeadInTheWater]

What's better settling near stone, and further its improvement yields, or on it? In my current game i settled on a stone tile so i was just in range of a nearby fish tile and so I'am on the coast with access to a desired body of water that i don't have from my other cities at the moment. Next closest coast tile puts me out of range of the fish or i could settle inland and lose benefits of being on the coast.

 

[Aqinu]

The decisions that I personally make is in function of:
1) If you have enough production and low food then you can settle on stone, if opposite settle near it (food is much easier to access, i.e. coast/ocean tiles, triangle of farms...)
2) Having cities on the coast depends on map type (most inland cities for Pangaea, continents and most coastal for islands, small continents), and to have enough coastal cities for minimal defense with some ships if you don't need a big navy in near future (most useful for amphibious attacks)

 

[Bromar1]

I think if you settled on stone, you can still get the +2 production from stoneworks on your city tile