I'm not sure about coffee but tea never quenches my thirst, only water or squash really does that for me.
I do find that when I first start the "drink lots of water" thing that I drink a lot and wee a lot but then after a week I find I don't need to go to the loo quite as often and my thirst is quenched easily.
It may just be your body getting used to its new intake, or you may need to up your water in take?
I always have a large glass of water before a meal too to stop me gorging on my food. Does anyone else do that?