Obviously we might have different aesthetic tastes OP so this might not be helpful to you, but I prefer the look of the cloth (rinsed well and wrung out, so is essentially clean but slightly damp) folded neatly and then draped over the edge of the sink, so it is a bit on the worktop and a bit hanging into the sink. A bit like a throw being folded and then draped over the edge/arm of the sofa.
(I am not personally a fan of the look of caddies in open plan, as I like the kitchen to look as much like it is part of the living area as possible.)