Having just finished Eleven’s run, I’m clear that in spite of Clara, Amy was his best and closest friend. In much the same way as both Nine and Ten gave their hearts to Rose, Eleven’s to the end belonged to Amy. Nor are they the only ones; each Doctor seems to have his special companion, no matter how many others he may travel with.
The First Doctor of course has Susan. Though his granddaughter stayed with him for just a little over one season, there’s no doubting that she was special to him.
The Second Doctor’s can only be Jamie. Appearing in his second story, the ebullient Scot remained by his Doctor’s side until the bitter end. While others came and went, Jamie always stayed.
The Third Doctor’s special friend was Jo. Brilliant Liz and independent Sarah had little patience for the grandiose, show-off Doctor, but Jo adored every minute of him, and offered her life for him on more than one occasion.
The Fourth Doctor may be an exception. He lasted longer and traveled with more friends than any other, and he may instead have two that were special to him. Sarah Jane obviously remained in his hearts all the way to his tenth incarnation, but his partnership with Romana was likely the closest and most equal of any in all his lives.
The Fifth Doctor seemed to share affection equally among his friends, but I suspect he had a soft spot for Nyssa. Young but not a child, she nearly matched him in intelligence and compassion, and their friendship avoided the prickliness of his relationship with Tegan or Turlough or even Adric.
The Sixth Doctor had Peri. The Seventh Doctor had Ace. The Eighth Doctor on screen had only Grace, though he may have bonded more completely with one of his audio companions. Big Finish fans would know better, but I believe he declared his love for Charley Pollard before the end.
Nine and Ten were one and the same more than any other pair of regenerations, and the tie that bound them was Rose. From the moment he took her hand in the basement of Henrik’s, to his last goodbye on January 1, 2005, he was Rose’s Doctor to the core.
Eleven had Amy; Twelve has Clara. Whomever he may travel with in the future, she will hold a special place in his heart.