The first half of Series 6. Unseen, the Doctor has taken Amy and Rory back home after events on the planet Ember. They identify a number of journeys which the Doctor has made through history in their absence - to the 17th Century (where he gets his portrait painted, nude, and Charles II locks him up in the Tower of London), World War II (where he is incarcerated in a German POW camp), and Hollywood in 1939 (where he features in the Laurel & Hardy movie The Flying Deuces).
Journey 581: Date and location unknown to Utah, 2011.
Specifically, it is 22nd April. Amy, Rory and River have just seen the death of the Doctor from the future. The current Doctor has responded to the same written invites as his companions.
Journey 582: Utah, 2011, to Washington DC, 8th April 1969.
In order to track down Canton Everett Delaware III, the TARDIS materialises in the Oval Office of the White House. It arrives silently, and invisible initially. The Doctor claims that the scanner does not work when the ship is invisible. Once more, River seems to know the TARDIS better, and is able to get it to work.
Journey 583: Washington DC to Florida, 8th April, 1969.
Canton joins the time-travellers as they journey to Florida, the Doctor working out an address from something which the mysterious little girl has said to President Nixon. The episode ends with the TARDIS is this location, and when we rejoin events for part two, some time has passed.
Journey 584: Florida, April 1969, to Area 51, Nevada, July 1969.
The TARDIS may have moved around in the intervening months, but if so there's nothing on screen. We "see" it next in the Doctor's cell - invisible once again.
Journey 585: Nevada to New York, July 1969.
The Doctor takes the TARDIS to intercept River's leap from a skyscraper. She is able to fall all the way through to the swimming pool.
Journey 586: New York to Cape Kennedy, Florida, July 1969.
The Doctor takes his companions to the Apollo 11 launch site.
Journeys 587 - 588: Cape Kennedy to Washington DC to Cape Kennedy, July 1969.
Presumably Amy and Canton travel by conventional means to find the orphanage. River must take the ship back to Washington DC in order to collect Nixon and bring him back to Florida to get the Doctor out of trouble after he gets arrested whilst planting his transmitter in the command module.
Journey 589: Cape Kennedy to Washington DC, July 1969.
The Doctor returns President Nixon to the Oval Office.
Journey 590: Washington DC to Graystark Hall orphanage, July 1969.
The Doctor, Rory and River join Canton at the orphanage, but find that Amy has been abducted. They succeed in capturing a Silent.
Journeys 591 - 592: Graystark Hall to Area 51, Nevada, July 1969.
The injured Silent is taken to the Doctor's cell. There is an unseen journey where President Nixon is collected once again from Washington DC - possibly en route.
Journey 593: Area 51 to Florida, July 1969.
The Doctor, Rory and River return to the location where the little girl had been kept in order to search for clues as to Amy's whereabouts, and to learn more about the astronaut suit.
Journey 594: Florida to location unknown, 9th July, 1969.
The TARDIS travels to the Silents' base, possibly still in Florida, where Amy has been held captive. It is the day of the Moon landing.
Journey 595: Silent base to Washington DC, July 1969.
Canton is taken back to the Oval Office and the Doctor says farewell to President Nixon.
Journey 596: Washington DC, 1969, to Stormcage Prison, 52nd Century.
The Doctor takes River back to prison. When the Doctor tells her that it is the first time she has kissed him, she realises that the time for her to reveal her true identity is imminent.
Journey 597: Stormcage Prison, 52nd Century, to unknown region of space, date unknown.
Rory is helping the Doctor with some repairs when he gets distracted by a combination of Amy's ever so short skirt and the glass floor of the console area... The TARDIS manages to materialise within itself thanks to some temporal glitch.
Journey 598: Unknown region of space, date unknown, to The Fancy, location unknown, 1699.
The TARDIS materialises in the hold of Captain Avery's ship, in some unspecified part of the ocean.
Journey 599: The Fancy - our universe to parallel one, 1699.
The ship goes out of control, forcing the Doctor and Avery to evacuate. The ship then travels on its own to the parallel dimension abutting this one - arriving in the hidden alien vessel.
Journey 600: The Fancy (parallel dimension), 1699, to unknown region of space, date unspecified.
The TARDIS is in space when there is a knock at the door. It marks the arrival of a Time Lord message cube.
Journey 601: Unknown region of space, date unknown, to House, bubble universe, date unknown.
The message cube takes the TARDIS to a small bubble universe, where it materialises on the planetoid known as House. This turns out to be a powerful TARDIS-eating intelligence. The planetoid is littered with the wrecks of numerous (disguised) TARDISes. We learn about the TARDIS Matrix, which is removed and deposited in a woman named Idris. This "soul" of the ship allows the TARDIS to communicate with the Doctor. She reveals that she "stole" the Doctor - rather than the other way round. Also, she is the reason why the TARDIS always seems to arrive at moments of crisis. She is annoyed that the Doctor ignores the "pull" instruction on the doors. (Of course, this actually refers only to the phone cabinet).
Journey 602: House planetoid to normal universe, date unknown.
House takes over the TARDIS with Amy and Rory trapped aboard. It takes the ship back into our universe in search of other TARDISes to feed upon. Idris is able to communicate telepathically with Rory. House is able to play with the temporal and spatial dimensions within the ship to torment Amy and Rory. The ship saves previous versions of the control room (more than have ever been seen on screen). The Doctor and Idris build a makeshift TARDIS from spare parts (showing that the outer shell does not have to be complete to function safely). They are reunited with Amy and Rory in the control room used by the Ninth and Tenth Doctors. A defence mechanism puts them back in the current control room, where the Matrix is able to re-enter the ship. It overwhelms and destroys House. Amy and Rory's bedroom gets deleted. It transpires they had bunk beds. The Doctor fails to confirm if he has a bedroom. The Matrix gives the Doctor a sign that it can still communicate with him, even though it is back in the ship.
Journey 603: Unknown region of space, date unknown, to St John's Monastery, 22nd Century.
The monastery sits on an island off the British coast. It is used as an acid mine / refinery. The acid causes the ship to sink into the ground. It later drops into the chamber where the Doctor and his companions just happen to have become trapped by the Flesh Jennifer creature.
Journeys 604 - 605: St John's Monastery to unknown location then to Morpeth Jensen HQ, 22nd Century.
The Doctor takes Jimmy to a beach to be reunited with his son on his birthday. He then takes Cleaves and Dicken to the company's HQ so they can attend a press conference and speak up for Ganger rights. Rory discovers that Amy has been swapped with a Flesh duplicate.
Journey 606: Morpeth Jensen HQ, Earth, 22nd Century, to 12th Cyber Legion, 52nd Century.
The Doctor and Rory begin their quest to find Amy by dropping in on the Cybermen, as they monitor what goes on in this region of space - 20,000 light years from Earth.
Journey 607: 12th Cyber Legion, 52nd Century, to London, 1888.
The Doctor next travels to Victorian London to enlist the help of the crime-fighting Silurian Madam Vastra, and her maid Jenny.
Journey 608: London, 1888, to Zaruthstra, 41st Century.
The Doctor next collects the Sontaran nurse Strax from the battle here.
Journey 609: Zaruthstra, 41st Century, to Stormcage prison, 52nd Century.
Rory is sent to enlist the help of River, but she declines. She knows the day has come when the Doctor will learn who she is. There is a mention of a future journey for the Doctor - taking her to a frost fair on the pre-embankment Thames in London, and a birthday song from Stevie Wonder.
Journey 610: Stormcage, 52nd Century, to the Maldovarium, location unknown, 52nd Century.
The Doctor's final on screen call is to the trading / leisure establishment run by Dorium Maldovar.
Journey 611: Maldovarium, to Demons Run, 52nd Century.
The Doctor takes his group of friends to the fortified asteroid where Amy has been held captive. There are a number of unseen journeys prior to the Doctor's arrival, as we see Silurian and Judoon forces, Prof Bracewell's space-going Spitfire fighters, and Captain Avery and his crew are also present.
Then there are other unseen journeys where the Doctor takes some of them home again, as at the conclusion of this episode, the TARDIS is in plain view - which it couldn't have been when he first arrived. River turns up and drops her bombshell...