Advantages of a city at the mouth of a major river
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   I want to stress out a difference between building a city near a river and close to a river. River tiles are great, as they give you additional gold and production. That is especially useful when a golden age kicks in, as even a tile with one production/gold yield will give you an additional one, thus increasing income from that tile two times.

The thing is your city doesn't necessarily have to be next to a river to work those river tiles. It can be a tile or even two away and still have access to them.

The only reason you would want your city to be next to a river are then available buildings, which are: water mill, garden and hydro plant. Water mill (+2 food) is a very low priority building, especially with maritime city states and taking you would still have an option of granary. Garden (+25% Great people) is useless unless you specialize that city specifically for great people generation. Hydro plant (+25% production) is not that necessary, as you would still have options of other type power plants.

So basically when settling try to get access to river tiles, but not necessarily settle right next to a river if otherwise you could get access to some resources or other valuable tiles.

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