It was Limbo from the first scene; Cobb washed ashore to his subconscious (projected as a beach). He and Saito speak of being old men, dying alone, full of regrets, and regret is the key to Cobb's "box". Everyone has a box, a vault, or a safe that represents the core of their subconscious, and Cobb's is the hotel room at the basement level via his Elevator of Regret. The "kick" signal song also represents his regret: Edith Piaf's song “Non, Je Ne Regrette Rien”. Cobb's reality is an elaborate projection in Limbo.

Ariadne and her team were sent in to bring him out. To plant an idea deep in his mind, the idea that led him to come to grips with his guilt and regret of his dead wife; basically the REAL inception to trick Cobb's own mind into thinking he came up with it himself, that he needs to let Mal go.

Ariadne's only failure I think was in failing to bring Cobb back out with her. Instead, he fell deeper into his own Limbo in which he now lives happily thinking he is reunited with his children. That top kept spinning, even tho it wobbled once or twice, but that could be explained as Cobb's faith in his own delusion.

Even I'm not 100% sure my theory is correct. Hell, everything that happened up to the airport scene could have really happened outside of Cobb's own mind, but like Ariadne said to Cobb. “The deeper we go into Fischer, the deeper we go into you."