In Episode II Anakin goes to the Lars homestead and meets his extended family. How would sending Luke there be "hidden" to Vader in any way? At least Leia had a random planet and family.
- Anakin/Vader hated Tatooine and preferred to avoid it.
- Anakin grew up there and had a strong influence on the place, so any sense of feeling a Force presence there could be discounted to his own influence.
- The best place to hide anything is in plain sight (see Edgar Allan Poe's The Purloined Letter for more on this).
- We develop a blindness to ourselves and our environment. Vader/Anakin is so familiar with Tatooine, there's a good chance, out of familarity, he wouldn't look too closely at the planet.
- If you were hiding something from Darth Vader, where's the one place you would figure he'd never dare you would hide it?
Quite honestly, this is a bad artifact of a retcon of what Lucas had originally intended as the backstory for Luke and his family.
Based on the notes and original novelizations, there is no evidence that Anakin was originally intended to be from Tatooine, and Owen Lars was not related to Anakin in any way. Owen was intended to be Ben's brother.
This was obviously changed by the time the prequels rolled around, but going by the the originally intended backstory, everything makes more sense with Ben hiding Luke on his own home planet, away from Anakin.
From the annotated screenplays:
It was decided during story meetings that Uncle Owen was in fact Ben's brother. Owen always resented Ben for imposing Luke on them, and now Ben is taking the blame for what is happening and is feeling guilty.
The original novelizations reflect this. From a 1993 (read: pre-SE, pre-prequels) printing of the Return of the Jedi novelization:
Ben continued his narrative. "When your father left, he didn't know your mother was pregnant. Your mother and I knew he would find out eventually, but we wanted to keep you both as safe as possible, for as long as possible. So I took you to live with my brother Owen, on Tatooine... and your mother took Leia to live as the daughter of Senator Organa, on Alderaan."
This is covered in the film's junior novelisation.
- Tatooine is physically far from the Empire
- Tatooine is ruled by the Hutts who are unlikely to welcome a substantial Empire presence on the planet
- Tatooine is already tainted by the Force (due to Anakin's association with the planet)
- They simply have a lack of safe options given recent events
“To Naboo, send her body,” Yoda said. “Pregnant, she must still appear. Hidden, safe, the children must be kept.”
“Someplace where the Sith will not sense their presence,” Obi-Wan said.
“Split up, they should be.”
Bail Organa raised his head. “My wife and I will take the girl. We’ve always talked of adopting a baby girl. She will be loved with us.”
Hidden in plain sight, Obi-Wan thought, and nodded. “What about the boy?”
“To Tatooine. To his family, send him.”
Remembering that harsh, dry planet, Obi-Wan winced. But there was nowhere else, and Tatooine was a world on the margins — the Hutt crime lords who ruled it had never been part of the Galactic Republic, and they would keep their distance from the Empire as well. “I will take the child there, and watch over him,” Obi-Wan said. He looked at Yoda, wanting reassurance he knew Yoda could not give him. “Master Yoda, do you think Anakin’s twins will be able to defeat Darth Sidious?”
The official novelisation also offers a couple of other reasons;
- The child needs to be raised in a loving environment.
- Living on Tatooine will offer Luke the opportunity to grow up in a similar environment to his father, learning physical as well as emotional toughness.
Bail stood, a little jerkily, as though he simply could no longer keep his seat. His flush had turned from embarrassment to pure uncomplicated joy. “Thank you, Masters-I don’t know what else to say. Thank you, that’s all. What of the boy?”
“Cliegg Lars still lives on Tatooine, I think-and Anakin’s stepbrother … Owen, that’s it, and his wife, Beru, still work the moisture farm outside Mos Eisley …”
“As close to kinfolk as the boy can come,” Yoda said approvingly. “But Tatooine, not like Alderaan it is-deep in the Outer Rim, a wild and dangerous planet.”
“Anakin survived it,” Obi-Wan said. “Luke can, too. And I can-well, I could take him there, and watch over him. Protect him from the worst of the planet’s dangers, until he can learn to protect himself.”
I always figured it was because even though there was an obvious link, Tatooine is far out on the outer rim and it was easy for Obi-wan to hide there, look over Luke and continue his studies in the Force. Anakin would have no desire to ever return there after what happened and he thought the child of him and Padme was dead with her. He would never have suspected that he indeed had a live child and that it was placed with his adopted family. The Lars weren't blood relatives of his.
I feel like it is a number of reasons. The first that came to mind for me though was that it is a safe option; in a galaxy where planets are at risk of being destroyed, putting him on Tatooine, his father's home planet, maybe guaranteed that his home planet wouldn’t fall victim.