First Comic Appearance: Astonishing X-Men (3rd series) #25
INTRODUCTION
For years, the X-Men had operated out of the X-Mansion located in Westchester, New York. Other than a brief stint in the Australian Outback, the X-Men had always called this home. That was until the first mutant since M-day was born. In the intervening hours, there was a mad scramble by various factions, X-Men included, to control the baby. During the final showdown, Xavier was seemingly killed and the mansion was destroyed. After suffering such bitter losses, Cyclops saw no way forward for the X-Men and he disbanded the team, letting the various members go their own ways. After some time off, Cyclops decided to re-assemble the X-Men but he wasn’t sure how or where. His answer would almost drop into his lap. Martinique Jason, the daughter of the villain Mastermind, had cast an illusion over San Francisco, making them believe it was the 1960s again. After Cyclops and a small team freed the city from the illusion, the mayor invited the X-Men to live there. San Francisco was seen as a place which was more tolerant to the mutant plight.
LOCATION
It was soon decided not to have the base within the main city of San Francisco. Rather, the Marin Headlands were selected for a number of reasons. It was difficult to get to, it was built to military specifications and it was not densely populated. The Marin Headlands themselves are a spit of land coming off the coast from San Francisco, California and is linked to the mainlaind by the Golden Gate Bridge. In its history, the area was used to conduct military operations, and as such a number of abandoned military buildings and bunkers litter the area.
FACILITIES
The surface level of Graymalkin Industries was relatively benign compared to what was under the ground. Cyclops designed it to look more like a community center or an embassy. The only other surface structures belonging to the X-Men were the entrances to the tunnels from which the Blackbird jets were deployed. 
Three miles below was where the real X-Men base was located. As they were using reclaimed buildings, the space was already there, they were just fitting it with everything they needed. As they were building it from scratch, they had the opportunity to try and make everything as environmentally friendly as possible. The base’s power came from solar arrays, as well as hydrokinetics within the bay itself. It was intended that the base would start paying out into the power grid again within a year.
As well as the tunnels for the Blackbird jets, the base also had a series of tunnels that spread out under the bay area of the city. Using more conventional transport, they could be downtown within ten minutes if they needed to be.
The base itself was designed with much of the same facilities as the X-Mansion. All the equipment within was state of the art and utilized holographic display screens amongst other technology.
[Click on the thumbnails for a larger version of each blueprints. All blueprints from the Astonishing X-Men Sketchbook.]
The following facilities could be found within the base:
HISTORY
After deciding to move there, the X-Men bought up all the disused military bases in the Marin Headlands and quickly began converting them into a base. With a lot of money and help, they built it up enough so that they could move in. One of the first things they did was have Mayor Sadie take a tour around. They showed her all the facilities and she was suitably impressed. However, she dropped a bomb on them by saying one of the local artists had decided to honor the X-Men’s move there. He had got his hands on three decommissioned Sentinels and had turned them into an art exhibit. They attended the opening of the exhibit, which ended up turning into a giant welcome party for the X-Men, with civilians dressing up as various members of the team. The party was crashed by Magneto, who restarted the Sentinels and sent them after the X-Men. After that incident, Cyclops decided it was time to gather the rest of the team. He had Emma Frost send out a telepathic message, though he didn’t just send it to all the X-Men. Rather, he sent it to every mutant across the world. He invited them to San Francisco as it was now a sanctuary for mutants. [Uncanny X-Men (1st series) #500]
Mutants began to flock to San Francisco after the telepathic call. Some stayed at the Graymalkin base, whilst others were more content to live with the city itself. 
Unfortunately, with the mutants also came trouble. A new threat in the form of the Madelyne Pryor was working in the shadows. She manipulated Empath into psychically attacking Emma and also set up the Hellfire Cult, who beat Pixie unconscious. After a stint in the infirmary, Pixie personally ended up taking down Empath, who was imprisoned within the X-Men’s base. [Uncanny X-Men (1st series) #501-502]
More residents slowly drifted in with Angel and Beast recruiting a team of scientists which would be dubbed X-Club. [Uncanny X-Men (1st series) #504-508] After Donald Pierce manipulated the Young X-Men into attacking the former members of the New Mutants, both teams relocated to the base with Pierce being kept prisoner there. [Young X-Men #6] Unbeknownst to everyone else, Emma Frost had Sebastian Shaw captured and placed in a holding cell within the base as well. [Uncanny X-Men Annual (2nd series) #2]
Things were already starting to turn sour already though. When a tape depicting the Cooperstown massacre was leaked to the press, the X-Men came under unwanted attention. Simon Trask used it to stir anti-mutant sentiment up again. He was trying to rally public support for Proposition X, which if ratified would limit mutants’ rights to procreate. [Uncanny X-Men (1st series) #505, 509]
Eventually, the time came for Madelyne Pryor to unleash the endgame to her plan. Currently trapped in an incorporeal form, she intended to create a new body for herself, using a piece of Jean Grey’s hair, something which Wolverine actually possessed. Sent by Madelyne into the Graymalkin base whilst the X-Men slept, the Sisterhood took the X-Men by surprise and escaped with the hair. Fortunately, the X-Men not only ultimately thwarted Madelyne’s plans to return, but in the process were reunited with their former teammate Psylocke, who rejoined the team. [Uncanny X-Men (1st series) #509-511]
Simon Trask and his Humanity Now! organization had been busy stirring up anti-mutant sentiments. When his group marched on San Francisco, they were met with the inevitable resistance, which led to riots around the city. Norman Osborn, current leader of HAMMER, used the unrest as an opportunity to deal with the X-Men by sending in his “Dark Avengers” to deal with the situation. Osborn’s Avengers mainly succeeded in making matters worse, though Osborn was pleased that Cyclops had now become an outlaw and the Beast had been captured.
Over the previous months, Osborn had been in secret contact with Emma Frost, with whom he had made a bargain. If she kept the X-Men out of his way, in return he would stay out of theirs. With their deal now broken, Osborn offered a different bargain, with her leading her own group of X-Men that he had chosen. This line-up mostly consisted of current or former villains and, though the group already showing cracks from the outset, Emma led them to defeat Trask’s new type of human Sentinel hybrids. However, when Osborn directed Emma and his X-Men against Cyclops and the true X-Men, Emma switched sides, revealing herself to be a double-agent attempting to gather information on Osborn’s intentions. Several of the "Dark X-Men" sided with Emma against Osborn as well.
Knowing that the incensed Osborn planned to bring the full weight of HAMMER down on them, Cyclops knew the X-Men were on the ropes with threats from all around. As such, he decided to enact a backup plan and ordered his science club to raise one of Magneto’s old asteroid bases off the seabed. After turning the tide on Osborn, Cyclops publicly declared that the mutant race would move out of America and set up their own community on the asteroid base, now an island off the San Francisco coast. [Utopia crossover]
Graymalkin Industries was abandoned in favor of the new island nation of Utopia. Much of the facility was stripped down and moved to the new base. The surface buildings did come in useful when the X-Men were quarantined with a weaponized virus. Whilst they were confined to Utopia, Kate Kildare held a press conference in the community center in a bid to inform the residents of San Francisco of the current situation. [Uncanny X-Men (1st series) #532]
RESIDENTS & TEAMS OPERATING OUT OF THE BASE
Most of the teams that operated out of Graymalkin Industries also called it home, but a few did choose to live within the main city itself.
The “astonishing” X-Men team were the first team to use the base. The team consisted of Armor, Beast, Cyclops, Emma Frost, Storm and Wolverine. [Astonishing X-Men (3rd series) #25]
When the X-Men had split up, some of the students formed their own team called the Young X-Men. Although the team was manipulated into forming by Donald Pierce, they chose to stay together after he was found out. They moved to the Graymalkin base and began operating out of it. The team consisted of Anole, Blindfold, Cipher, Dust, Graymalkin and Rockslide. Ink was another member of the team at this point, although he remained in a coma in the infirmary. [Young X-Men #6]
When Legion was brought back to life, some of the original New Mutants were placed in danger. The rest reformed their old team to go on a rescue mission. After they succeeded in saving their teammates, Cyclops allowed them to stay together, as they functioned well as a strike team for the X-Men. Cannonball, Karma, Magik, Magma, Mirage and Sunspot were the team members during the Graymalkin period. Legion was briefly taken there as well when he was defeated by the New Mutants. [New Mutants (3rd series) #1]
Once the X-Men settled into life at the base, Angel and Beast decided to form a science club to collect some of the brightest minds together to aid in mutant affairs. The roster included Doctor Nemesis, Kavita Rao, Madison Jeffries and Yuriko Takiguchi. They mostly operated within the labs and infirmary located on site. [Uncanny X-Men (1st series) #504-508]
Wolverine’s secret X-Force team didn’t use the base to meet up in but the members did stay there. As well as Angel and Wolverine, the roster also had Domino, Elixir, Warpath and X-23. Wolfsbane and Vanisher were also members of the team at the time but they were never shown to be at Graymalkin Industries. [X-Force (3rd series) #1]
Cyclops made sure the base had a school for the students. As well as the ones on a team, the student body included Bling!, Gentle, Glob Herman, Hellion, Indra, Loa, Match, Mercury, Onyxx, Pixie, Prodigy, Stepford Cuckoos, Surge and Trance. After Cyclops reformed the X-Men, not all the students returned immediately or at least they were not shown on panel.
As well as the members serving on the splinter teams or within the student body, Boom Boom, Colossus, Dazzler, Hepzibah, Nightcrawler, Northstar and Psylocke also stayed there. Many of these served as members of the main team and were deployed as and when they were needed.
The X-Men ended up taking a number of prisoners too. Empath, who was a minion of Madelyne Pryor, was placed in the brig. [Uncanny X-Men (1st series) #502]. Donald Pierce was captured as well, [Young X-Men #5] and Sebastian Shaw was secretly placed in the brig after Emma faked his execution. [Uncanny X-Men Annual (2nd series) #2]