Before we begin our look at each of the TARDIS' on screen journeys through Space and Time, it might be useful to consider what we know of where it might have travelled before we first caught sight of it, sitting in a corner of I.M. Foreman's junkyard at 76 Totters Lane. How did it get there? Thanks to The Name of the Doctor, we know that the Doctor was already well into his first incarnation when he and Susan "stole" the ship from a repair bay in the Capitol on Gallifrey. It appears he was guided to that particular Type 40 time capsule by Clara Oswin, and that the ship itself deliberately allowed itself to be taken (The Doctor's Wife).
We know that the ship did not travel directly from Gallifrey to London, 1963, as a number of other journeys are mentioned very early on by the Doctor and Susan - which must pre-date Totters Lane, as they are obviously news to Ian and Barbara.
As the series has progressed, more and more unseen adventures get a mention. It is not always possible to deduce exactly when these took place. Only when a specific companion is mentioned as having been present can we be clear, or if a companion is the one telling a third party about it - e.g. Rose telling Mickey about Woman Wept in Boom Town. We know that the Doctor's unseen visit to Karfel was in his Third incarnation - thanks to someone having painted his portrait, and a locket with Jo Grant's picture in it. We assume that it was in his Fourth incarnation that he got drunk with Azmael on a previous visit to Jaconda if we take the Doctor's "couple of regenerations ago" literally - and, frankly, because it sounds a lot more like the Fourth Doctor than any other up to this point.
Between Gallifrey and Totters Lane, a handful of journeys are definitely known. The majority of these seem to have been to different periods of Earth's history.
Susan sees a mistake in a book about the French Revolution and this, along with the fact that it is supposed to be the Doctor's "favourite" period, implies they visited France at this time before Ian and Barbara were taken there. This might have been when the TARDIS disguised itself as a sedan chair. The Doctor met Pyrrho - founder of scepticism. Perhaps that was when the TARDIS appeared as an ionic column. (These disguises could equally have been entirely different visits). The Doctor and Susan also encountered Henry VIII, when the ship needed to be retrieved from the Tower of London. We also know that the Doctor and Susan experienced a Zeppelin air raid, and that the Doctor was with James Watt when he had his revelation about the potential of steam power. At some point, he was given an ulster coat by Gilbert and Sullivan.
When we get to that encounter between the Doctor and the Mountain Mauler of Montana, however, this could well be an unseen adventure post Totters Lane - as he is speaking to Vicki, and Ian and Barbara are not present to give us any clues one way or the other.
Of the few non-Earth destinations visited by the TARDIS prior to London, 1963, we have a trip to the planets Dido, Quinnis, and Esto. Susan claims to have seen the metal seas on Venus. A more recent mention of the early travels of the Doctor and Susan came in The Rings of Akhaten.
And so, onto the televised journeys of the TARDIS.
Journey 001: 76 Totters Lane, London, 1963, to an unknown location on Earth, c. 100,000 BC.
This dematerialisation is unlike any that will follow. From what we see on the scanner, the ship seems to take off vertically - the surrounding streets seen from above and diminishing. The ship will travel upwards only very occasionally in the future. The lights dim. Most significantly, the take-off seems distinctly uncomfortable for the Doctor and Susan - and renders Ian and Barbara temporarily unconscious.
The landing location is not known. (We are only taking the date from an alternative story title).
As well as the Chameleon Circuit breaking down, the Yearometer has also failed.
We now know that the reasons that the Doctor can't pilot the ship accurately are three-fold:
1. He doesn't fully understand it.
2. The TARDIS is nearing obsolescence and had been in for repairs when taken.
3. Sometimes the ship takes him where he needs to go, rather than where he wants to go.
Journey 002: Earth c. 100,000 BC to Skaro, date unknown.
The TARDIS materialises in the middle of the petrified forest on Skaro within seconds of leaving its last destination - the Doctor and his companions are practically still out of breath from fleeing the Tribe of Gum. The radiation meter takes its time to register, and only flashes. (There really ought to have been some audible alarm as well - maybe another technical failure).
The Doctor makes a number of excuses for not knowing where - or when - they are, and for being unable to get back to the London of 1963. Is there really no star chart / navigation system on board?
Journey 003: Skaro, date unknown, to location unknown - possibly the Solar System 4.5 billion years ago.
The stuck Fast Return switch has taken the TARDIS back towards the creation of a solar system. The date above refers to our own, if it was heading back to Earth, though the scanner implies that it is Skaro's system. Only a bright light can be seen from the TARDIS doors when they open.
Journey 004: Location unknown to the Himalayas, 1289.
On landing, the ship suffers a catastrophic power failure. Coveted by Marco Polo as a gift for Kublai Khan, the ship is manually transported across the Plateau of Pamir, the Gobi Desert, then through Tun-Huang, Sinju, Cheng-Ting and Shang-Tu to arrive in Peking.
When travelling across the desert, condensation forms inside the ship - so the systems do at least appear to be waterproofed.
Journey 005: Peking, 1289, to an island on Marinus, date unknown.
The TARDIS appears to materialise silently - something it will do occasionally throughout the Hartnell era. This is the first time we have not seen the ship arrive at its new destination at the end of the previous adventure - so scope for unseen adventures between? Unlikely, as Ian is still wearing the previous story's costume. Also, later on in The Sensorites, the Doctor and his companions will reminisce about their adventures so far and this implies no unseen stories at this point.
Journey 006: Marinus, date unknown, to Mexico, c. late 15th Century.
The TARDIS materialises in the tomb of Aztec High Priest Yetaxa. There is nothing to suggest that this is the Aztec capital - present day Mexico City - as there is no mention of any ruler. Montezuma or one of his fellow kings would surely have wanted to meet the reincarnation of Yetaxa.
Journey 007: Mexico, late 15th Century, to Earth spaceship in the vicinity of planet Sense-Sphere, 28th Century.
Another reason for believing that the Doctor and Susan have not done a huge amount of travelling, other than through Earth's history, is the puzzlement the Doctor experiences when arriving on Captain Maitland's spaceship. They have landed and yet are still moving. Seems to be the first materialisation on a spaceship.
Back on Skaro, Susan explained that the TARDIS lock had a defence mechanism, whereby if the key wasn't fitted exactly right, the lock would melt. The Sensorites simply remove the whole lock. When Ian suggest breaking the down the doors, the Doctor states that this would destroy the internal dimensions - maybe rendering the craft the same size inside as out, as will happen later on.
Journey 008: Earth spaceship (?), 28th Century, to France, July 1794.
The Doctor and his companions viewing the departure of Maitland's ship on the scanner does seem to imply that they are not actually on it themselves. Has the TARDIS possibly been manhandled down to the Sense-Sphere unseen? Maybe taken down to have the lock re-affixed.
The TARDIS materialises in a forest somewhere to the north of Paris (Stirling / Le Maître can take them part of the way on his route to the Channel - and Barbara conveniently points it out on a map). The date can be fixed from the inclusion of Robespierre's downfall in the story.
Season One ends with the TARDIS dematerialising from the French bois on journey 009 - but that's for next time...