Per the series 6 finale
The Wedding of River Song , the TARDIS was in his eye.
Where 'his eye' is in fact the Teselecta's eye, as the thing we thought was the future Doctor was in fact just the Teselecta.
The Doctor was inside, along with his TARDIS.
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Well, consider that the TARDIS is a living thing, and moreover one that is in love with the Doctor.
She could always just throw herself into a sun or land on some remote asteroid, but that still leaves the chance (however small) that someone might run into her and remember.
To correct what appears to be an oversight, consider also what happens during "The Parting of the Ways" (or is it the one just before that?).
The Doctor sends Rose home in the TARDIS and (by way of his answering machine), tells her to just leave it, essentially letting it die.
His description of how it will be forgotten and ignored could explain why the existence of the Cowboy Hat Doctor's TARDIS isn't a big deal.
Additionally, does another TARDIS in the universe actually mess anything up?
If you think about it, almost any time the Doctor does anything , there's at least one other Doctor out there with a corresponding TARDIS.
Time travel does not lend itself well to avoiding multiples of oneself.
scifi.stackexchange.com/users/2230/Jack Henahan
Consider Rule Number One:
The Doctor Lies.
With that in mind, we don't know that the Cowboy Hat Doctor is who he claims (or the age he claims) at this point
and he may be the "Oblivious" Meet-in-the-Diner Doctor
we see later who just staged earlier events for the benefit of that one figure on the hill who was watching and whom Amy saw, then forgot.
In other words, we really know nothing about Cowboy Hat Doctor, much less that he got there in a later or earlier version of the Tardis.
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We first see that particular version of the Doctor without the TARDIS (and in a cowboy hat?).
Given that, it's fairly safe to assume that until we find out otherwise, the Doctor most likely arrived in some other fashion, considering we weren't given evidence that the TARDIS is around.
It does beg the question - where is the TARDIS at that point in time?
Considering it's likely the Doctor won't actually follow that full timeline and die, we may not ever know.
EDIT:
As Keen states, the Doctor does not actually die, but he is present when the Teselecta is "killed.
" The implication is that the Doctor and the Teselecta traveled to the location in the TARDIS, then the Doctor and TARDIS relocated into the Teselecta's eye.
scifi.stackexchange.com/users/1913/Ian Pugsley
Well, perhaps this isn't in the spirit of the question, but I suspect that the most accurate answer will turn out to be "because the writer didn't think of that."
Made all the more glaring by the fuss they make over disposing of the body.
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Maybe the future version of the doctor fixed the chameleon circuit and the car is the Tardis!
Not really likely, but it would work. :-)
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Wikipedia notes that: In the Big Finish audio play Omega, the Doctor meets a TARDIS which "dies" after its Time Lord master's demise.
So, it's possible that a TARDIS tends to die when its Doctor dies.
scifi.stackexchange.com/users/2380/hairboat
There is not such a thing as a extra TARDIS.
The fixed point was that the Doctor pretended his death, but to enyone the fixed point is that the Doctor is dead.
There is not such a thing as a machine that extract the fixed points in timeand explain them.
In other words, what it was written to happen in the Lake Silencio
was that the Doctor is going to pretend his death, and when River stop this "act", that fixed point, it cause a paradox breaking the fixed point.
And that act, is what Amy, Rory, Canton and River see in the first time, that "first death".
scifi.stackexchange.com/users/36665/Kmi
The following question is about the S6E1 episode of Doctor Who,  The Impossible Astronaut , where we see a character for a few minutes.   At the start of the episode we meet a future Doctor.  He proceeds to die shortly thereafter.  But he had to have gotten to Earth and that time somehow.  Usually he travels via TARDIS, so where's his TARDIS?  There should be an extra TARDIS parked on Earth somewhere.
Where's the extra TARDIS?
scifi.stackexchange.com
<doctor-who><tardis>
scifi.stackexchange.com/questions/3981
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 The implication is that the Doctor and the Teselecta traveled to the location in the TARDIS, then the Doctor and TARDIS relocated into the Teselecta's eye. Some say there is no such thing as an extra TARDIS, and that a TARDIS tends to die when its Doctor dies. Debate rages about what happened to TARDIS when Dr Who died. Some believe TARDIS relocated with the DR in the Teleselecta's eye. Others say TARDIS died with the doctor. Regarding an extra TARDIS, it seems there is no such thing.
It could be that the Dr and the TARDIS are in the Teleselecta's eye. It could also be that TARDIS dies when the Dr dies. There is no extra TARDIS.