It probably stayed in the Forbidden Forest.
In 1999, shortly after the publication of Prisoner of Azkaban in the US, JK Rowling was asked about the Ford Anglia:
Will we ever hear from Mr. Weasley's car again?
Yes, you will hear from Mr. Weasley's car again, but yet again, I'm not telling you how.
— Barnes and Noble chat transcript (September 1999)
This never came to pass – the car is not mentioned again in the books. I’m also unaware of any interviews or Pottermore releases that discuss the car’s fate.
When the car picks up Harry and Ron in the Forbidden Forest, Ron observes that it seems to have acclimatised to Forest living:
“It’s been here all the time!” said Ron delightedly, walking around the car. “Look at it. The forest’s turned it wild….”
and the last we see of it is when it returns to the Forest:
Harry gave the car a grateful pat as it reversed back into the forest and disappeared from view.
Lacking further information, I’d assume it’s still there. Given that it’s gone wild, I think it’s unlikely it would return to the Weasleys. It probably can’t find its way home, and if it did, it would return to being trapped and immobile in their garage. Now it has a taste of freedom, why would it go back?
I assume the plotline Rowling had in mind involved somebody returning to the Forest and finding the car, and I have a few guesses:
- The shenanigans with Grawp and Umbridge in Order of the Phoenix.
- The battle of Hogwarts in Deathly Hallows: there were strong rumours that the car was going to make an appearance in the film adaptation, but they never came to pass.
but without confirmation from JK Rowling, I don’t think there’s much else we can say.