Within the main canon of Star Wars (the 6 theatrical movies, Clone Wars TV series and film and Rebels TV series) there was no account of Anakin returning to Tatooine after becoming Darth Vader however in the latest Marvel comic series Star Wars : Darth Vader, we learn that he did indeed travel to Tatooine to converse with Jabba the Hutt and hire bounty hunters to search out the identity of the "mysterious pilot".
The main EU novel dealing with Darth's rise to power is Dark Lord: The Rise of Darth Vader. This book was written in consultation with LucasArts and contains a considerable amount of information about the gap between Revenge of the Sith and A New Hope. In it, Obi-Wan learns (from Qui-Gon's force ghost) that Vader will never set foot on Tatooine again, supposedly making it an ideal place to hide young Luke:
“Qui-Gon!” he said. “Master!” Realizing that the locals were quickly
going to brand him a madman if they heard him talking to himself, he
ducked into the narrow alley between two stores. “Master, is Darth
Vader Anakin?” he asked after a moment.
Yes. Although the Anakin you and I knew is imprisoned by the dark
“I was wrong to leave him on Mustafar. I should have made sure he was
The Force will determine Anakin’s future. Obi-Wan: Luke must not be
told that Vader is his father until the time is right. “Should I take
further steps to hide Luke?”
The core of Anakin that resides in Vader grasps that Tatooine is the
source of nearly everything that causes him pain. Vader will never set
foot on Tatooine, if only out of fear of reawakening Anakin.
Obi-Wan exhaled in relief. “Then my obligation is unchanged. But from
what Yoda told me, I know that I have much to learn, Master.”
You were always that way, Obi-Wan.
Obviously in light of the recent canon changes, this assurance now seems rather more hollow.