Where is Obi-Wan's lightsaber?

No. Obi-Wan Kenobi gives Anakin's lightsaber to Luke.

More specifically, Obi-Wan gives Anakin's second lightsaber to Luke.

You can see Anakin holding it in his left hand.

You can see in this screenshot that it is the same one that Luke is given.

Obi-Wan also had a blue lightsaber from before the Fall of the Republic.

This is the one he uses against Vader aboard the Death Star.

As to why Luke's lightsaber looks white, I will direct you to the question Why were some lightsaber effects in A New Hope different quality?. In specific, DVK's answer explains the evolution of the errors in blade colors in the movies.

He definitely didn't lose his lightsaber.

In G-canon, he uses it to cut off Ponda Baba's arm (first limb cut in the published order in the long list of limb-cutting in TGFFA).

In C-canon, in the "Kenobi" novel, he used it to fight Sand People right after landing on Tatooine with baby Luke.

lemme splain to you..

Anakin had built a new lightsaber before Ep. 3 and lost it when defeated by Obi-Wan. Obi kept it and his own lightsaber until he gave Luke his father's saber and lost his own when he was struck down by Vader.

Luke kept his father's lightsaber in the Millenium Falcon when he rescued Leia and began training after the destruction of the Death Star. He trained with Yoda for a few days and left for Bespin after using his lightsaber many times on Hoth. Had Hoth not happened, Luke may not've become as good a swordsman as people claim. Experience counts. Once Luke fought Vader on Bespin, he lost his hand and Anakin's lightsaber. (what a shame)

When Luke retreated from Bespin and had his new hand constructed, he went into a cave on Tatooine and constructed a new lightsaber very similar to Obi-Wan's except it had a green blade and a lot more chrome. Luke kept that lightsaber essentially for the rest of his life, even through the foundation and uprising of The New Jedi Order.