Eye of Orion
The Eye of Orion was known to be one of the most tranquil places in the universe. Tegan Jovanka likened it to "Earth after a thunderstorm." According to the Fifth Doctor, it achieved its calming effects from the "high bombardment of positive ions." (TV: The Five Doctors)
It may have been an entire planet — based largely on the Sixth Doctor's insistence that its beautiful moonset was the "ideal tonic for the weary time traveller" — but was at least a specific spot on a planet. (AUDIO: Arrangements for War)
The Fifth Doctor deliberately took Turlough and Tegan to the Eye immediately after their encounter with the Master and Kamelion in the time of King John. Turlough had been there before on his own. (TV: The King's Demons) While there, the Doctor updated the look of the TARDIS console. Soon after stepping out of the newly-refurbished TARDIS, the Doctor experienced "cosmic angst", before discovering that his past selves were being separated from him. (TV: The Five Doctors)
The trio returned to the Eye and were about to play cricket when a Raston Warrior Robot, delivered by Ryoth's use of a Time Scoop, attacked them. They hid behind rubble until they were joined by the Eighth Doctor. Using the principle of Buridan's ass, they approached the robot with an equal distance between them and the robot. Confused as to whom to target and their similarity, the robot deactivated. (PROSE: The Eight Doctors)
The Sixth Doctor delighted in bombarding his companions with tales of the Eye, but had difficulty actually going there. It would have been the first destination to which the post-regenerative Sixth Doctor would have taken Peri Brown, but he had trouble remembering the co-ordinates. (TV: The Twin Dilemma)
Later in their travels, Peri was so tired of his hype she preemptively blocked the suggestion of the Eye as a suitable holiday spot: "I've heard all about that elusive place once too often." She suggested that the Eye had no native life-forms and that even tourists were scarce. When the Doctor described Andromeda — by which he might have meant either the constellation or the galaxy — as having "some of the most magical sights in the entire universe: astral starbursts creating a myriad celestial bodies against a timeless royal blue backdrop", Peri said he always described the Eye of Orion in precisely the same way. (TV: Timelash)
Likewise the Sixth Doctor made several promises to take Evelyn Smythe to the Eye, but never managed to do so. In one of the two accounts of Melanie Bush meeting Evelyn, the then-former companion Evelyn specifically asked that he take her home by way of the Eye. Mel, for her part, was the only companion of the Doctor ever described as having actually visited the Eye. (PROSE: Instruments of Darkness)
The Seventh Doctor and Ace sat and meditated on the Eye of Orion during their search for the Timewyrm. (PROSE: Timewyrm: Revelation)
Martha Jones may have visited the Eye, as well. She wrote that it had been a thriving holiday resort, but after the Last Great Time War was converted into a shrine of the war, with only a small memorial, nameless due to the many who died in the war. At this point, the only other structures were scattered ruins. During its time as a shrine to the war, the Eye of Orion was still and quiet, covered in ruins, grass and mist. The Tenth Doctor apparently imparted details about the Time War to Martha whilst there. (Martha Jones's Myspace blog)
After defeating House, the Eleventh Doctor suggested to Rory that they go to "somewhere restful" like the Eye of Orion, but admitted that he wasn't terribly "good at restful". He left it up to the TARDIS to choose whether the Eye was where he needed to go. The TARDIS set a course and dematerialised, but it was unclear whether they made it to the Eye on this occasion. (TV: The Doctor's Wife)
