Eye of Orion
The Eye of Orion was known to be one of the most tranquil places in the universe. Tegan likened it to "Earth after a thunderstorm." According to the Fifth Doctor. it achieved its calming effects from the "high bombardment of positive ions." (DW: 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. (BFA: Arrangements for War)
The Doctor deliberately took Turlough and Tegan to the Eye immediately following their encounter with the Master and Kamelion in the time of King John (DW: 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 began to experience what he called "cosmic angst", before discovering that his past selves were being separated from him.
The Doctor seemed to delight in bombarding his companions with tales of the Eye, but had difficulty in actually going there. It would have been the first destination to which the post-regenerative Sixth Doctor would have taken Peri, but he had difficulty remembering the co-ordinates (DW: The Twin Dilemma).
Later in their travels, Peri was so fatigued by his hype that she preemptively blocked the suggestion of the Eye as a suitable holiday spot, saying, "I've heard all about that elusive place once too often." She further suggested that the Eye had no native life-forms and that even tourists were scarce. When the Doctor described Andromeda 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 that he always described the Eye of Orion in precisely the same way. (DW: Timelash)
Likewise the Sixth Doctor made several promises to take Evelyn Smythe to the Eye, but never managed to succeed. 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. (PDA: Instruments of Darkness)
The Doctor and Ace sat and meditated on the Eye of Orion during their search for the Timewyrm. (NA: Timewyrm: Revelation)
The Doctor once met his fifth self at the Eye, where they defeated a Raston Warrior Robot sent to kill them by Ryoth. (EDA: The Eight Doctors)
Martha Jones may have visited the Eye, as well. She wrote that it used to be a thriving holiday resort, but after the Last Great Time War, it was converted into a shrine of the War, with only 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 Doctor apparently imparted details about the Time War to Martha whilst there. (Martha Jones's Myspace blog)