Being a newly appointed Sith Lord, Darth Vader built his first lightsaber on the lava-filled planet of Mustafar, located in the outer-rim territories. It was actually a stolen lightsaber from Jedi Master Infil'a that he tried to make his own. It was only fair that Sidious commanded him to go to Mustafar for this process, as it was where Siths would bleed their crystals and make their lightsabers. Not to mention, being a Sith holy site, this planet flowed with the Dark powers and also had the Sith temple.