How can I cancel the quest to kill Paarthurnax?

When the blades ask you to kill Paarthurnax (the dragon or the leader of the Greybeards) where are they located so that I can cancel that mission and tell them that I don't want to kill him.

You can ignore that quest and continue. Killing paathurnax will fix your status with the Blades, but the Greybeards will no longer help you. Not killing will cause the Blade to not help you.

You can't. You have to go confront Paarthurnax to continue the main story. There is no way to cancel this quest.

However, Paarthurnax speaks to you and offers you alternatives to killing him, which you may take him up on.

If you are trying to play through the Blades' storyline without killing Paarthurnax, you simply can't.

It's a choice you need to make in the game. It's like going with the Imperials versus the Stormcloaks. You just have to choose.

Either way, you're not really missing out on much. Both the Greybeards and Esbern will give you locations of word walls. The Blades are a bit more interactive, though (recruiting followers, dragon-killing missions, the like).

If you were on the PC, there is a neat little mod called (aptly) The Paarthurnax Dilemma. This mod would allow you to play both sides of the fence: Paarthurnax can live, but you can still play the Blades questline.