The first to leave, oddly enough, was Splinter.
The Ancient One invited him to live in Japan and look after his home while he was away on Tribunal business. Everyone involved knew it was a working retirement, a chance for the old rat to live in the land of his birth and be close to his Master Yoshi. His sons were happy for him, eventually, after insinuating with varying degrees of tact that they weren't sure it was a good idea. Finally he informed them that he wasn't that old and that he'd be all right without them. He informed them more quietly, one by one and in reassuring tones, that they would be all right without him.
The next to leave was Donatello.
The Utroms had contacted Leatherhead shortly after the defeat of the Shredder, having been overjoyed to learn that he was still alive, and offering him a place with them. He had reluctantly refused, feeling that his friends the turtles needed him more. They had kept in touch and, as a result of Leatherhead's insistence about Donatello's genius, eventually offered them both a place. Donatello had gone quiet then, and reminded his brothers of his experiences in the world where Shredder was lord and master. He had disappeared, leaving the three of them alone, and though he knew that it was not their future, still he hesitated, the words "I guess we really needed that level head of yours" echoing through his mind but never through his lips. They told him he was being stupid and practically pushed him out the door, letting him see the tears staining their masks as they did so.
After that it was only the three of them for a long time. Splinter wrote often, and Donatello had set up a communications device before he left, and he could visit frequently using the transmat. But it wasn't the same, even though their father and brother were both immensely happy where they were: Splinter finally able to relax and live for himself, Donatello finally able to share his genius with those who would appreciate it.
Then Leonardo left.
He was even more reluctant than Donatello, not even telling his brothers of the Daimyo's offer to come to the Battle Nexus and formally tutor his son in the ways of ninjitsu. They eventually found out through Usagi, and Don made a special trip home to help convince Leo to take this opportunity. They had all known Leo would never be happy in a life that did not involve ninjitsu, and he had been slowly wilting ever since Splinter left. Raphael and Michelangelo promised, Scout's honor, eyes rolling, that they wouldn't do anything stupid while he was gone, and then later they remade that promise formally and seriously, in Japanese, which Leo seemed to trust more.
Raph and Mike left at the same time.
Neither of them could stand the thought of being down there alone, the last of his brothers, and being down there just the two of them was depressing enough. Mike took the basement apartment at April's, eventually becoming a fairly successful webcomicker. Raph wandered around the country on his bike for months at a time before ending up back in New York with his brother, only to take off again with little to no warning. Don made a tracking device that fit onto his shell, and made him promise never to take it off. As far as they could tell, he never did.
They might have chosen anywhere to gather; after all, they now had a multitude of places to choose from. But whenever they wanted to be together, all of them, it was always at the old lair, dusty and dank though it had become. Mike and April had only so much extra time to devote to maintaining what was essentially a ghost house, after all. But they never saw the filth or age that encroached on their old home. All they could see were the memories.