While we the viewers make the acquaintence of the Doctor and his granddaughter Susan at the same time and place as the schoolteachers Ian Chesterton and Barbara Wright, down in a scrapyard in Totter's Lane in 1963, all sorts of hints are dropped throughout the first three seasons that they had their share of adventures before then.
For example, during The Edge of Destruction, the TARDIS' viewscreen shows the planet they visited immediately prior to Totter's Lane: Quinnis. Somewhere out in the 4th universe, the duo nearly lost the timeship that they permanently and illegally borrowed from the dockyards on Gallifrey. Other planets included Venus, where they had seen its molten metal oceans, and a planet with a telepathic screaming jungle like that on Esto in The Keys of Marinus.
On a few ocassions, they ended up revisting places they had been to before. The Doctor had been to Rome before arriving again in The Romans. In The Reign of Terror, we learn that the French Revolution is one of his favorite eras. While still a student at Coal Hill, Susan even corrected a history textbook on it. Nor was The Rescue the Doctor's first visit to the planet Dido. He enjoyed the company of those peace-loving people a century before.
They had visited England in the future - hence Susan forgetting that 1963 England was not yet using metric - and during World War I, during which they witnessed a Zeppelin raid. Strangely, they couldn't be kept out of the country. Henry the VIII sentenced the Doctor to the Tower of London, and Gillbert and Sullivan gave him his coat. In Regency London he received a fashion compliment from Beau Brummell. Joining the British, they were present at the Seige of Mafeking during the Boer War.
It was not only the places that were notable, but the historical figures. The Doctor taught skepticism to Pyrrho the Greek, the application of steam to James Watt, the story of "The Emperor's New Clothes" to Hans Christian Andersen, and wrestling to "The Mountain Mauler of Montana". All this from someone who would go on to chastize Barbara and condemn the Monk for trying to change history! However, the Doctor also had a first and very brief encounter with a future villain, the Celestial Toymaker.
And this is just between the Doctor and Susan's flight from Gallifrey and their taking on passengers in the scrapyard! What happened before then? Who did the Doctor marry? Who were his children? What kind of relationship did he have with his granddaughter that would cause them to abscond with a TARDIS together? Was it his idea or her's? And what the heck is his real name?!