The Medical Facility in the Kamakura Area in the Elfen Lied series may not be only one facility, no indicator of it being multiple locations is given.
This building has a depiction in some form in both versions of the series. Looking neither decrepit nor very modern, it seems to be a full-blown hospital. The cast members find themselves there more often during the manga series than in the anime. Likely, since their train to Hokkaido was likely not far out of Gokurakuji Train Station, the traumatized Kouta, as well as the bodies of Kanae and their father, were taken there, after Lucy attacked them. It is also likely that, had Kouta and Yuka sought care for Lucy/Nyu's head wound in the early part of the story, they would have brought her there.
In both versions, the first we see of this facility is when Kouta (and version depending, Yuka) is injured by Bando when he attempts to recapture Lucy/Nyu and answers questions from police detectives who are also searching for Lucy. Despite a bandaged head, Kouta is well enough to leave with Yuka that night to go back to Maple House.
It is unknown but possible that the wounded Bando went to the same facility. It is also possible that this is where his castration was to have taken place after his outfitting with bionic replacements for his hands and eyes. In his unique fashion, Bando prevented the castration from taking place.
The next time it is shown, again in both versions, is when a desperate Mayu, injured during the bloody battle between the awakened Lucy and Nana, calls Kouta to pick her up, despite at this point barely knowing him. This pick-up seems to have been either through the Emergency Room entrance or perhaps suggests a smaller clinic in the same area. Again, the narrative gives no indication. Mayu promises to pay a bill that Kouta paid for her, though this rapidly becomes moot. The bill could not have been too costly, and Kouta's concern is why Mayu called him, instead of her parents. The facility is not seen again in the anime, though it is possible this is where Isobe takes Mariko while she is recovering after Nana temporarily removes her powers.
The facility is a focus of activity for a few chapters of the manga after Maple House is invaded by forces loyal to Chief Kakuzawa, this time successfully recapturing Lucy, though at a high cost to all involved. Kouta, who was shot by the Agent for threatening Nousou, is unconscious while regaining his lost memories. Mayu, Wanta, and Yuka seem only to be shaken up, and Nana's injuries heal faster because she is Diclonius. They are visited there by Yuka's Mother, who, while concerned about the group, questions whether Nana should continue living with them, given what they learned of the girl they called Nyu. Nozomi, her throat injured by a chokehold applied by a soldier, is watched over in a separate room, with her father perhaps determined to keep her away from her friends at Maple House, regarding them as a danger. Nozomi is later shown to be at home at a time when Kouta is still supposed to be under care, though he too had left.
In another part of the facility (though again, this could have been a separate building as well), Nousou is recovering from multiple wounds, watched over by the Agent. At this point, it seems possible the Agent had all injured brought to the same facility. This joint relocation was possibly made to keep an eye on the residents of Maple House pending possible legal charges for harboring Lucy. Otherwise, wishing to control who the residents spoke to or regarding their part in this as done, the Agent wanted to know where they were. Since Lucy at that point had been sent back to the Diclonius Research Institute for her final confrontation with Chief Kakuzawa, the Maple House residents likely were not an issue. The usually cold Doctor Nousou had begun to show paternalistic feelings towards his four viable clones of Mariko Kurama, Alicia, Barbara, Cynthia, and Diana, all of whom had suffered injuries related to the invasion of Maple House, and two of whom had died at that point while saving his life. Wishing to do the right thing by Barbara, the only one of the three present clones to survive Lucy's wrath, Nousou freed her from a device meant to make her docile. Barbara, whose actual personality (and possibly that of her clone sisters as well) was bitter, resentful and acutely aware of how she was treated, found a friendly nurse and promptly decapitated her. Tossing the nurse's head in Nousou's lap, Barbara explained her hatred and resentment before killing an apologetic Nousou. Barbara then leaped off the roof of the medical facility, using her powers to push herself off the ground, flattening cars as she flew, seeking to punish Nana for living among Humans. The facility is last seen again in this part of the story as Mayu and Yuka discover that Kouta has left his recovery bed, gone to have it out with Lucy/Nyu.
In the story's conclusion, while Lucy/Nyu's sacrifice healed Kouta's life-threatening wounds after he was shot again, this time by Kurama, he needed to return to the hospital to complete his recovery. Depicted doing so, by this point well known to the staff, while using a cane to walk, Kouta leaves. This scene is the final appearance of the facility in the series, though perhaps Kouta's daughter Nyuu was probably born in this facility.
As with many elements of the series, a lack of specifics makes it impossible to say whether each or any instance of a medical facility was this one or whether each one was meant to be separate. It is also impossible to say how well it was equipped compared to the real Kamakura's facilities or if the unique events of the series meant it was better equipped than other similar hospitals.